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{SECT 0 {PARA 256 "" 0 "" {TEXT 289 90 "Precalculus Exploration 6 Exer
cises: General Sinusoids Reference Function Shifted by [h,k]" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 290 111 "In each exerc
ise 1-8 below you are given two plots and each plot contains two graph
s, a red reference function " }{TEXT 302 4 "f(x)" }{TEXT 303 30 ", and
 a blue shifted function " }{TEXT 304 4 "g(x)" }{TEXT 305 2 ". " }}
{PARA 0 "" 0 "" {TEXT 301 72 "Plot 1. On the first plot of each exerci
se, your red reference function " }{TEXT 295 4 "f(x)" }{TEXT 296 7 " i
s an " }{TEXT 293 9 "unshifted" }{TEXT 294 1 " " }{TEXT 291 4 "sine" }
{TEXT 292 30 " function, your blue function " }{TEXT 297 4 "g(x)" }
{TEXT 298 6 " is a " }{TEXT 299 12 "shifted sine" }{TEXT 300 117 " fun
ction (obtained from the red function), and you are to write down the \+
correct expression (formula) for each one. " }{TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT 316 72 "Plot 2. On the first plot of each exercise, your
 red reference function " }{TEXT 310 4 "f(x)" }{TEXT 311 7 " is an " }
{TEXT 308 9 "unshifted" }{TEXT 309 1 " " }{TEXT 306 6 "cosine" }{TEXT 
307 30 " function, your blue function " }{TEXT 312 4 "g(x)" }{TEXT 
313 6 " is a " }{TEXT 314 14 "shifted cosine" }{TEXT 315 117 " functio
n (obtained from the red function), and you are to write down the corr
ect expression (formula) for each one. " }{TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 260 22 "Exercise 1. Sine Model" }{TEXT -1 1 " " }}{PARA 13 "" 1 
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45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 333 24 "Exercise 4. Cosine Model" }{TEXT -1 0 "" }}{PARA 13 "" 
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{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 321 22 "Exercise 5. Sine Model" 
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0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 334 24 "Exercise 5. Cosine Model" }{TEXT -1 0 "" }}{PARA 13 "" 
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45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
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-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 335 
24 "Exercise 8. Cosine Model" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" 
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45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 338 
116 "In each exercise 9-16 below you are given only one plot and each \+
plot contains two graphs, a red reference function " }{TEXT 339 4 "f(x
)" }{TEXT 340 30 ", and a blue shifted function " }{TEXT 341 4 "g(x)" 
}{TEXT 342 150 ". In each of these exercises you need find the functio
ns for only one model, sine or cosine, and the one you should use is i
ndicated in each exercise." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 325 22 "Exercise 9. Sine \+
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&F7$\"\"&F7" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "
Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "
Curve 8" "Curve 9" "Curve 10" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 
327 23 "Exercise 11. Sine Model" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 
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{TEXT -1 1 " " }{TEXT 343 25 "Exercise 15. Cosine Model" }}{PARA 13 "
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\"3ISi9`\"=g&GFen7$Fgn$\"3>W?\">e\"*f+$FenFD-%&TITLEG6$%ZEx.16~Cosine~
Model:~~Reference~function~shifted~by~[h,~k]G-F96%F;F<\"#9-%+AXESLABEL
SG6%%!GFfhq-F96#F<-%*AXESTICKSG6$\"\"(\"\"*-%%VIEWG6$;$!$c#!\"\"$\"$c#
Fdiq;$!+++++^F,$\"+++++^F," 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 65 "Ex. 1 Sine & Cosine Models:  Reference function shifted b
y [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 256 79 "Sine Models:  Referen
ce function shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 2646 "restart:\nExnum:=1:\nmaxht:=4:    # Enter
 the max value of the graph of the data (a peak)\nminht:=0:   # Enter \+
the min value of the graph of the data (a valley)\np:=4:        # Ente
r the period p = distance between two successive peaks (or valleys)\nh
:=-1:        # Enter the h = the distance the reference sine curve is \+
translated right(left)\nj:=2:        # Enter j = the number of cycles \+
that you want.\nn:=1:        # Enter n = the number of new functions t
hat you want different from sin(x).  \na:=(maxht-minht)/2: # The ampli
tude a = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\nb:=
2*Pi/p:          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The
 central axis axis = (max+min)/2\nk:=axis:     # k = the distance the \+
reference sine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p
:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->
a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i
*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference fu
nction:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=
red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x
-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nf
i:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xle
ft/2,ytop-.01,`Reference function`],\n                        font=[HE
LVETICA,DEFAULT,12],\n                        color=red,align=\{BELOW,
CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted func
tion`],\n                        font=[HELVETICA,DEFAULT,12],\n       \+
                 color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[t
extplot]([xright-.01,axis+.09,`axis `],\n                        font=
[HELVETICA,DEFAULT,12],\n                        color=blue,align=\{AB
OVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,
color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nl
inep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot(
[[0,0]],style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]
],style=point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n \+
          [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],lin
ep[3],\n            pointp[1],pointp[2],\n            seq(plt[i],i=0..
n)],\n            #labels=[`t (sec)`,`V (volts)`],\n            labels
=[``,``],\n            tickmarks=[9,9],\n            #view=[x_left..x_
right,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEF
AULT,14],\n            title=`Ex.`||Exnum||` Sine Model:  Reference fu
nction shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:  \+
 p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;
\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-
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$%WEx.1~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F96%F;F<\"#
9-%*AXESTICKSG6$\"\"*F]jq-%+AXESLABELSG6%%!GFajq-F96#F<-%%VIEWG6$;FUFY
;$!\"'F)$\"\"'F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 
0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve
 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'
/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG\"\"%/%$~~bG,$*&F%!\"\"%#PiG\"
\"\"F//%9~Shift~right~(left):~~~hGF-/%6~Shift~up~(down):~~~kGF%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&
\"\"#\"\"\"-%$sinG6#,$*(F*!\"\"%#PiGF+F'F+F+F+F+/,&-%6~Shifted~functio
n:~~fG6#,&F'F+F+F+F+F*F+,&*&F*F+-F-6#,$*(F*F1F2F+F8F+F+F+F+F*F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 257 82 "Cosine Models:  Reference functions shifted by [h, k]:  \+
f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2651 "res
tart:\nExnum:=1:\nmaxht:=4:    # Enter the max value of the graph of t
he data (a peak)\nminht:=0:   # Enter the min value of the graph of th
e data (a valley)\np:=4:        # Enter the period p = distance betwee
n two successive peaks (or valleys)\nh:=0:        # Enter the h = the \+
distance the reference cosine curve is translated right(left)\nj:=2:  \+
      # Enter j = the number of cycles that you want.\nn:=1:        # \+
Enter n = the number of new functions that you want different from cos
(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:  \+
           # The frequency f = 1/p\nb:=2*Pi/p:          # The factor b
 = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/
2\nk:=axis:     # k = the distance the reference cosine curve is trans
lated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\n
ytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:
\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF
[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plo
t(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h
,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=
xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=
F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference fun
ction`],\n                        font=[HELVETICA,DEFAULT,12],\n      \+
                  color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[
textplot]([xright/2,ytop-.01,`Shifted function`],\n                   \+
     font=[HELVETICA,DEFAULT,12],\n                        color=blue,
align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.0
9,`axis `],\n                        font=[HELVETICA,DEFAULT,12],\n   \+
                     color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot
([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot
([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],
linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=c
ircle,color=blue):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,
color=blue):\nSinPlot1:=plots[display](\n           [txtp[1],txtp[2],t
xtp[3],\n            linep[1],linep[2],linep[3],\n            pointp[1
],pointp[2],\n            seq(plt[i],i=0..n)],\n            #labels=[`
t (sec)`,`V (volts)`],\n            labels=[``,``],\n            tickm
arks=[7,9],\n            #view=[x_left..x_right,y_vertex-20..y_vertex+
20],\n            titlefont=[HELVETICA,DEFAULT,14],\n            title
=`Ex.`||Exnum||` Cosine Model:  Reference function shifted by [h, k]`)
:\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift righ
t (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 
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XESTICKSG6$\"\"(\"\"*-%&TITLEG6$%YEx.1~Cosine~Model:~~Reference~functi
on~shifted~by~[h,~k]G-F96%F;F<\"#9-%%VIEWG6$;FUFY;$!\"'F)$\"\"'F)" 1 
2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve
 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve
 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"
\"#/%-~Period:~~~pG\"\"%/%$~~bG,$*&F%!\"\"%#PiG\"\"\"F//%9~Shift~right
~(left):~~~hG\"\"!/%6~Shift~up~(down):~~~kGF%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$cos
G6#,$*(F*!\"\"%#PiGF+F'F+F+F+F+/,&-%6~Shifted~function:~~fGF&F+F*F+,&*
&F*F+F,F+F+F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 65 "Ex. 2 Sine & Cosine Models:  Refe
rence function shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 261 
79 "Sine Models:  Reference function shifted by [h, k]:  f(x) = a*sin(
b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2645 "restart:\nExnum:
=2:\nmaxht:=4:    # Enter the max value of the graph of the data (a pe
ak)\nminht:=2:   # Enter the min value of the graph of the data (a val
ley)\np:=8:        # Enter the period p = distance between two success
ive peaks (or valleys)\nh:=0:        # Enter the h = the distance the \+
reference sine curve is translated right(left)\nj:=2:        # Enter j
 = the number of cycles that you want.\nn:=1:        # Enter n = the n
umber of new functions that you want different from sin(x).  \na:=(max
ht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:             # Th
e frequency f = 1/p\nb:=2*Pi/p:          # The factor b = 2*Pi/p\naxis
:=(maxht+minht)/2: # The central axis axis = (max+min)/2\nk:=axis:    \+
 # k = the distance the reference sine curve is translated up(down)\nx
left:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2
*a+k):\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to \+
n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):
\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xr
ight,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=`
 Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=yb
ot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[
1]:=plots[textplot]([xleft/2,ytop-.01,`Reference function`],\n        \+
                font=[HELVETICA,DEFAULT,12],\n                        \+
color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/
2,ytop-.01,`Shifted function`],\n                        font=[HELVETI
CA,DEFAULT,12],\n                        color=blue,align=\{BELOW,CENT
ER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n     \+
                   font=[HELVETICA,DEFAULT,12],\n                     \+
   color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xr
ight,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],lin
estyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=
blue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):
\npointp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinP
lot1:=plots[display](\n           [txtp[1],txtp[2],txtp[3],\n         \+
   linep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n    \+
        seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts
)`],\n            labels=[``,``],\n            tickmarks=[9,9],\n     \+
       #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            \+
titlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` S
ine Model:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Ampli
tude:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` S
hift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 
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Fj[l7$Fdin$\"339&e90.,+#Fj[l7$Fiin$\"3%R'[W=@N,?Fj[l7$F^jn$\"3lf+Xpy*p
+#Fj[l7$Fcjn$\"3cmBG[a,<?Fj[l7$Fhjn$\"3w:&z6vg8.#Fj[l7$F][o$\"3'*y))=D
Jws?Fj[l7$Fb[o$\"3w\"**4bnw/8#Fj[l7$Fg[o$\"3M>5GUJ`#G#Fj[l7$F\\\\o$\"3
Yf?=ssl![#Fj[l7$Fa\\o$\"3S2Yx9Jz,EFj[l7$Ff\\o$\"3KoipY\"R.t#Fj[l7$F[]o
$\"3i#=!foK!R'GFj[l7$FY$\"3c**************HFj[lFC-%&TITLEG6$%WEx.2~Sin
e~Model:~~Reference~function~shifted~by~[h,~k]G-F86%F:F;\"#9-%+AXESLAB
ELSG6%%!GFhbq-F86#F;-%*AXESTICKSG6$\"\"*F^cq-%%VIEWG6$;FTFY;$!\"&F)$\"
\"&F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve \+
1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve \+
8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitud
e:~~~aG\"\"\"/%-~Period:~~~pG\"\")/%$~~bG,$*&\"\"%!\"\"%#PiGF%F%/%9~Sh
ift~right~(left):~~~hG\"\"!/%6~Shift~up~(down):~~~kG\"\"$" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG-%$sinG6#,$*(
\"\"%!\"\"%#PiG\"\"\"F'F0F0/,&-%6~Shifted~function:~~fGF&F0\"\"$F0,&F(
F0F5F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT 262 82 "Cosine Models:  Reference functions shifted by
 [h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 2651 "restart:\nExnum:=2:\nmaxht:=4:    # Enter the max value of the
 graph of the data (a peak)\nminht:=2:   # Enter the min value of the \+
graph of the data (a valley)\np:=8:        # Enter the period p = dist
ance between two successive peaks (or valleys)\nh:=2:        # Enter t
he h = the distance the reference cosine curve is translated right(lef
t)\nj:=2:        # Enter j = the number of cycles that you want.\nn:=1
:        # Enter n = the number of new functions that you want differe
nt from cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2
\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p:          # T
he factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis =
 (max+min)/2\nk:=axis:     # k = the distance the reference cosine cur
ve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+
1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:
\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i \+
= 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\n
plt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]
:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=p
lot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(Lis
t),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Re
ference function`],\n                        font=[HELVETICA,DEFAULT,1
2],\n                        color=red,align=\{BELOW,CENTER\}): \ntxtp
[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n        \+
                font=[HELVETICA,DEFAULT,12],\n                        \+
color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-
.01,axis+.09,`axis `],\n                        font=[HELVETICA,DEFAUL
T,12],\n                        color=blue,align=\{ABOVE,LEFT\}):\nlin
ep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlin
ep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h
,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=poi
nt,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=point,sym
bol=circle,color=blue):\nSinPlot1:=plots[display](\n           [txtp[1
],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n         \+
   pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n           \+
 #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n      \+
      tickmarks=[7,9],\n            #view=[x_left..x_right,y_vertex-20
..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n      \+
      title=`Ex.`||Exnum||` Cosine Model:  Reference function shifted \+
by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,`
 Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}
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C$F`]l7$Fhgn$\"3wX!)R1R*e6$F`]l7$Fbhn$\"3)4!G/wy*R)HF`]l7$F\\in$\"3ks$
fiF!*H'GF`]l7$Ffin$\"3^T#\\Nu+Su#F`]l7$F[jn$\"3TrO!*=>yGEF`]l7$F`jn$\"
3U5`:.4.>DF`]l7$Fejn$\"3$QujAi[?S#F`]l7$Fjjn$\"3[m\"*yA6j'H#F`]l7$F_[o
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F^\\o$\"3,\"GJpbrW.#F`]l7$$\"3ELL$=#oRu8FU$\"3p#GMH$*\\,-#F`]l7$Fc\\o$
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39&e90.,+#F`]l7$$\"3imm\">)=i19FU$\"3%R'[W=@N,?F`]l7$F]]o$\"3lf+Xpy*p+
#F`]l7$$\"3DLL3v9_B9FU$\"3cmBG[a,<?F`]l7$Fb]o$\"3w:&z6vg8.#F`]l7$Fg]o$
\"3'*y))=DJws?F`]l7$F\\^o$\"3w\"**4bnw/8#F`]l7$Ff^o$\"3M>5GUJ`#G#F`]l7
$F`_o$\"3Yf?=ssl![#F`]l7$Fe_o$\"3S2Yx9Jz,EF`]l7$Fj_o$\"3KoipY\"R.t#F`]
l7$Fd`o$\"3i#=!foK!R'GF`]l7$FY$\"3c**************HF`]lFC-%+AXESLABELSG
6%%!GFeiq-F86#F;-%*AXESTICKSG6$\"\"(\"\"*-%&TITLEG6$%YEx.2~Cosine~Mode
l:~~Reference~function~shifted~by~[h,~k]G-F86%F:F;\"#9-%%VIEWG6$;FTFY;
$!\"&F)$\"\"&F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 
0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve
 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'
/%/Amplitude:~~~aG\"\"\"/%-~Period:~~~pG\"\")/%$~~bG,$*&\"\"%!\"\"%#Pi
GF%F%/%9~Shift~right~(left):~~~hG\"\"#/%6~Shift~up~(down):~~~kG\"\"$" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG-%
$cosG6#,$*(\"\"%!\"\"%#PiG\"\"\"F'F0F0/,&-%6~Shifted~function:~~fG6#,&
F'F0\"\"#F.F0\"\"$F0,&-F)6#,$*(F-F.F/F0F6F0F0F0F8F0" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 65 
"Ex. 3 Sine & Cosine Models:  Reference function shifted by [h, k]" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 263 79 "Sine Models:  Reference function \+
shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2648 "restart:\nExnum:=3:\nmaxht:=3:    # Enter the max v
alue of the graph of the data (a peak)\nminht:=1:   # Enter the min va
lue of the graph of the data (a valley)\np:=6:        # Enter the peri
od p = distance between two successive peaks (or valleys)\nh:=-1/2:   \+
     # Enter the h = the distance the reference sine curve is translat
ed right(left)\nj:=2:        # Enter j = the number of cycles that you
 want.\nn:=1:        # Enter n = the number of new functions that you \+
want different from sin(x).  \na:=(maxht-minht)/2: # The amplitude a =
 (max-min)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p: \+
         # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central
 axis axis = (max+min)/2\nk:=axis:     # k = the distance the referenc
e sine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:
=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*sin(b*
(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x
):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function: \+
 f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\ne
lse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\n
plt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList
:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,yto
p-.01,`Reference function`],\n                        font=[HELVETICA,
DEFAULT,12],\n                        color=red,align=\{BELOW,CENTER\}
): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],
\n                        font=[HELVETICA,DEFAULT,12],\n              \+
          color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot
]([xright-.01,axis+.09,`axis `],\n                        font=[HELVET
ICA,DEFAULT,12],\n                        color=blue,align=\{ABOVE,LEF
T\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=b
lue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]
:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]]
,style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style
=point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n        \+
   [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],
\n            pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n
            #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,`
`],\n            tickmarks=[9,9],\n            #view=[x_left..x_right,
y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,1
4],\n            title=`Ex.`||Exnum||` Sine Model:  Reference function
 shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,
`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(Li
st);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%TEXTG
6'7$$!\"'\"\"!$\"$*R!\"#Q3Reference~function6\"%+ALIGNBELOWG-%'COLOURG
6&%$RGBG$\"*++++\"!\")$F)F)F7-%%FONTG6%%*HELVETICAG%(DEFAULTG\"#7-F$6'
7$$\"\"'F)F*Q1Shifted~functionF.F/-F16&F3F7F7F4F8-F$6(7$$\"%*>\"F,$\"$
4#F,Q&axis~F.%*ALIGNLEFTG%+ALIGNABOVEGFDF8-%'CURVESG6%7$7$$!#7F)$\"\"#
F)7$$F=F)FWFD-%*LINESTYLEG6#FX-FQ6%7$7$F7FW7$$!3++++++++]!#=FWFDFen-FQ
6%7$7$F]oF7F\\oFDFen-FQ6&7#7$F7F7FD-%&STYLEG6#%&POINTG-%'SYMBOLG6#%'CI
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k]G-F96%F;F<\"#9-%%VIEWG6$;FUFZ;$!\"%F)$\"\"%F)" 1 2 0 1 10 0 2 9 1 4 
2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curv
e 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}
{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"\"/%-~Period:~~~
pG\"\"'/%$~~bG,$*&\"\"$!\"\"%#PiGF%F%/%9~Shift~right~(left):~~~hG#F.\"
\"#/%6~Shift~up~(down):~~~kGF3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7
Reference~function:~~fG6#%\"xG-%$sinG6#,$*(\"\"$!\"\"%#PiG\"\"\"F'F0F0
/,&-%6~Shifted~function:~~fG6#,&F'F0#F0\"\"#F0F0F8F0,&-F)6#,$*(F-F.F/F
0F6F0F0F0F8F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 264 82 "Cosine Models:  Reference functio
ns shifted by [h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 2651 "restart:\nExnum:=3:\nmaxht:=3:    # Enter the max
 value of the graph of the data (a peak)\nminht:=1:   # Enter the min \+
value of the graph of the data (a valley)\np:=6:        # Enter the pe
riod p = distance between two successive peaks (or valleys)\nh:=1:    \+
    # Enter the h = the distance the reference cosine curve is transla
ted right(left)\nj:=2:        # Enter j = the number of cycles that yo
u want.\nn:=1:        # Enter n = the number of new functions that you
 want different from cos(x).  \na:=(maxht-minht)/2: # The amplitude a \+
= (max-min)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p:
          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The centra
l axis axis = (max+min)/2\nk:=axis:     # k = the distance the referen
ce cosine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nyb
ot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos
(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*
k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference functio
n:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):
\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k
:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nL
ist:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,
ytop-.01,`Reference function`],\n                        font=[HELVETI
CA,DEFAULT,12],\n                        color=red,align=\{BELOW,CENTE
R\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`
],\n                        font=[HELVETICA,DEFAULT,12],\n            \+
            color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textpl
ot]([xright-.01,axis+.09,`axis `],\n                        font=[HELV
ETICA,DEFAULT,12],\n                        color=blue,align=\{ABOVE,L
EFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color
=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[
3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0
]],style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],sty
le=point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n      \+
     [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3]
,\n            pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],
\n            #labels=[`t (sec)`,`V (volts)`],\n            labels=[``
,``],\n            tickmarks=[7,9],\n            #view=[x_left..x_righ
t,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT
,14],\n            title=`Ex.`||Exnum||` Cosine Model:  Reference func
tion shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p
`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;\no
p(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%T
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Fgu7$Fijn$\"3oW9Np@XN5Fgu7$$\"3&3+]7K?9\")*Fgu$\"3E$\\jF#fV>5Fgu7$F^[o
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#*G$H`s4J2\"Fgu7$Fg\\o$\"3@!ziQ)e)o7\"Fgu7$F\\]o$\"3Y\"4[![J3*>\"Fgu7$
Fa]o$\"3%)eZDs%p`G\"Fgu7$Ff]o$\"3_WtczpA%Q\"Fgu7$F[^o$\"3#yb@8l;R\\\"F
gu7$F`^o$\"3B::px$psg\"Fgu7$Fe^o$\"3FU*\\bz^ps\"Fgu7$Fj^o$\"3uhm]n\\.^
=Fgu7$F__o$\"31fWjG!>v(>Fgu7$Fd_o$\"3nxFXP0z8@Fgu7$Fi_o$\"3)GMK.`WzC#F
gu7$Fc`o$\"3AM2(*\\X[xBFgu7$FZ$\"3M(************\\#FguFD-%&TITLEG6$%YE
x.3~Cosine~Model:~~Reference~function~shifted~by~[h,~k]G-F96%F;F<\"#9-
%*AXESTICKSG6$\"\"(\"\"*-%+AXESLABELSG6%%!GFd\\r-F96#F<-%%VIEWG6$;FUFZ
;$!\"%F)$\"\"%F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 
0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve
 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'
/%/Amplitude:~~~aG\"\"\"/%-~Period:~~~pG\"\"'/%$~~bG,$*&\"\"$!\"\"%#Pi
GF%F%/%9~Shift~right~(left):~~~hGF%/%6~Shift~up~(down):~~~kG\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG-%$c
osG6#,$*(\"\"$!\"\"%#PiG\"\"\"F'F0F0/,&-%6~Shifted~function:~~fG6#,&F'
F0F0F.F0\"\"#F0,&-F)6#,$*(F-F.F/F0F6F0F0F0F7F0" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 65 "Ex. \+
4 Sine & Cosine Models:  Reference function shifted by [h, k]" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 265 79 "Sine Models:  Reference function \+
shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2650 "restart:\nExnum:=4:\nmaxht:=2:    # Enter the max v
alue of the graph of the data (a peak)\nminht:=-1:   # Enter the min v
alue of the graph of the data (a valley)\np:=10:        # Enter the pe
riod p = distance between two successive peaks (or valleys)\nh:=-1/2: \+
       # Enter the h = the distance the reference sine curve is transl
ated right(left)\nj:=2:        # Enter j = the number of cycles that y
ou want.\nn:=1:        # Enter n = the number of new functions that yo
u want different from sin(x).  \na:=(maxht-minht)/2: # The amplitude a
 = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p
:          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The centr
al axis axis = (max+min)/2\nk:=axis:     # k = the distance the refere
nce sine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybo
t:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*sin(
b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k
,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function
:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):
\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k
:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nL
ist:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,
ytop-.01,`Reference function`],\n                        font=[HELVETI
CA,DEFAULT,12],\n                        color=red,align=\{BELOW,CENTE
R\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`
],\n                        font=[HELVETICA,DEFAULT,12],\n            \+
            color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textpl
ot]([xright-.01,axis+.09,`axis `],\n                        font=[HELV
ETICA,DEFAULT,12],\n                        color=blue,align=\{ABOVE,L
EFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color
=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[
3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0
]],style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],sty
le=point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n      \+
     [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3]
,\n            pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],
\n            #labels=[`t (sec)`,`V (volts)`],\n            labels=[``
,``],\n            tickmarks=[9,9],\n            #view=[x_left..x_righ
t,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT
,14],\n            title=`Ex.`||Exnum||` Sine Model:  Reference functi
on shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=
p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(
List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%TEX
TG6'7$$!#5\"\"!$\"$*R!\"#Q3Reference~function6\"%+ALIGNBELOWG-%'COLOUR
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'7$$\"#5F)F*Q1Shifted~functionF.F/-F16&F3F7F7F4F8-F$6(7$$\"%**>F,$\"++
+++fF(Q&axis~F.%*ALIGNLEFTG%+ALIGNABOVEGFDF8-%'CURVESG6%7$7$$!#?F)$\"3
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-%&TITLEG6$%WEx.4~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F
96%F;F<\"#9-%*AXESTICKSG6$\"\"*Faeq-%+AXESLABELSG6%%!GFeeq-F96#F<-%%VI
EWG6$;FUFen;$!\"%F)$\"\"%F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 
1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG#\"\"$\"\"#/%-~Period:~~~pG\"#5/
%$~~bG,$*&\"\"&!\"\"%#PiG\"\"\"F2/%9~Shift~right~(left):~~~hG#F0F'/%6~
Shift~up~(down):~~~kG#F2F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Refe
rence~function:~~fG6#%\"xG,$*&#\"\"$\"\"#\"\"\"-%$sinG6#,$*(\"\"&!\"\"
%#PiGF-F'F-F-F-F-/,&-%6~Shifted~function:~~fG6#,&F'F-#F-F,F-F-F<F-,&*&
F*F--F/6#,$*(F3F4F5F-F;F-F-F-F-F<F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 82 "Cosine Model
s:  Reference functions shifted by [h, k]:  f(x) = a*cos(b(x - h)) + k
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2653 "restart:\nExnum:=4:\nmaxht:=2
:    # Enter the max value of the graph of the data (a peak)\nminht:=-
1:   # Enter the min value of the graph of the data (a valley)\np:=10:
        # Enter the period p = distance between two successive peaks (
or valleys)\nh:=2:        # Enter the h = the distance the reference c
osine curve is translated right(left)\nj:=2:        # Enter j = the nu
mber of cycles that you want.\nn:=1:        # Enter n = the number of \+
new functions that you want different from cos(x).  \na:=(maxht-minht)
/2: # The amplitude a = (max-min)/2\nf:=1/p:             # The frequen
cy f = 1/p\nb:=2*Pi/p:          # The factor b = 2*Pi/p\naxis:=(maxht+
minht)/2: # The central axis axis = (max+min)/2\nk:=axis:     # k = th
e distance the reference cosine curve is translated up(down)\nxleft:=-
j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):
\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n
#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt
[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y
=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shift
ed function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..yt
op,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=pl
ots[textplot]([xleft/2,ytop-.01,`Reference function`],\n              \+
          font=[HELVETICA,DEFAULT,12],\n                        color=
red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop
-.01,`Shifted function`],\n                        font=[HELVETICA,DEF
AULT,12],\n                        color=blue,align=\{BELOW,CENTER\}):
\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n           \+
             font=[HELVETICA,DEFAULT,12],\n                        col
or=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,a
xis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle
=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):
\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\npoin
tp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=
plots[display](\n           [txtp[1],txtp[2],txtp[3],\n            lin
ep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n          \+
  seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n
            labels=[``,``],\n            tickmarks=[7,9],\n           \+
 #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            titlef
ont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Cosine \+
Model:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amplitude
:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift
 up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 
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\\_o$!3)R^FIna_p#Fht7$Fa_o$\"3sMPI%>nAb\"FY7$Ff_o$\"3W@X3#HS6d$FY7$F[`
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TLEG6$%YEx.4~Cosine~Model:~~Reference~function~shifted~by~[h,~k]G-F96%
F;F<\"#9-%*AXESTICKSG6$\"\"(\"\"*-%+AXESLABELSG6%%!GFfhq-F96#F<-%%VIEW
G6$;FUFen;$!\"%F)$\"\"%F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG#\"\"$\"\"#/%-~Period:~~~pG\"#5/%$~~b
G,$*&\"\"&!\"\"%#PiG\"\"\"F2/%9~Shift~right~(left):~~~hGF'/%6~Shift~up
~(down):~~~kG#F2F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~fu
nction:~~fG6#%\"xG,$*&#\"\"$\"\"#\"\"\"-%$cosG6#,$*(\"\"&!\"\"%#PiGF-F
'F-F-F-F-/,&-%6~Shifted~function:~~fG6#,&F'F-F,F4F-#F-F,F-,&*&F*F--F/6
#,$*(F3F4F5F-F;F-F-F-F-F<F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 65 "Ex. 5 Sine & Cosine Mode
ls:  Reference function shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT 267 79 "Sine Models:  Reference function shifted by [h, k]:  f(x
) = a*sin(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2702 "restar
t:\nExnum:=5:\nmaxht:=3:    # Enter the max value of the graph of the \+
data (a peak)\nminht:=-3:   # Enter the min value of the graph of the \+
data (a valley)\np:=Pi:        # Enter the period p = distance between
 two successive peaks (or valleys)\nh:=Pi/6:      # Enter the h = the \+
distance the reference sine curve is translated right(left)\nj:=2:    \+
    # Enter j = the number of cycles that you want.\nn:=1:        # En
ter n = the number of new functions that you want different from sin(x
).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:    \+
         # The frequency f = 1/p\n#b:=2*Pi/p:          # The factor b \+
= 2*Pi/p\nb:=evalf(2*Pi/p,4):          # The factor b = 2*Pi/p\naxis:=
(maxht+minht)/2: # The central axis axis = (max+min)/2\nk:=axis:     #
 k = the distance the reference sine curve is translated up(down)\nxle
ft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a
+k):\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n \+
do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\n
Ftxt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xrig
ht,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` S
hifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot
..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]
:=plots[textplot]([xleft/2,ytop-.01,`Reference function`],\n          \+
              font=[HELVETICA,DEFAULT,12],\n                        co
lor=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,
ytop-.01,`Shifted function`],\n                        font=[HELVETICA
,DEFAULT,12],\n                        color=blue,align=\{BELOW,CENTER
\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n       \+
                 font=[HELVETICA,DEFAULT,12],\n                       \+
 color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xrig
ht,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],lines
tyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=bl
ue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\n
pointp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlo
t1:=plots[display](\n           [txtp[1],txtp[2],txtp[3],\n           \+
 linep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n      \+
      seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`
],\n            labels=[``,``],\n            tickmarks=[9,9],\n       \+
     #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            ti
tlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sin
e Model:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amplitu
de:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shi
ft up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 
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Ex.5~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-%
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$\"\"(F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Cur
ve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Cur
ve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Ampli
tude:~~~aG\"\"$/%-~Period:~~~pG%#PiG/%$~~bG$\"\"#\"\"!/%9~Shift~right~
(left):~~~hG,$*&\"\"'!\"\"F(\"\"\"F4/%6~Shift~up~(down):~~~kGF-" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&
\"\"$\"\"\"-%$sinG6#,$*&$\"\"#\"\"!F+F'F+F+F+F+/-%6~Shifted~function:~
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!#5F+F<F+F;F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 268 82 "Cosine Models:  Reference functio
ns shifted by [h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 2713 "restart:\nExnum:=5:\nmaxht:=3:    # Enter the max
 value of the graph of the data (a peak)\nminht:=-3:   # Enter the min
 value of the graph of the data (a valley)\np:=Pi:        # Enter the \+
period p = distance between two successive peaks (or valleys)\nh:=5*Pi
/12:        # Enter the h = the distance the reference cosine curve is
 translated right(left)\nj:=2:        # Enter j = the number of cycles
 that you want.\nn:=1:        # Enter n = the number of new functions \+
that you want different from cos(x).  \na:=(maxht-minht)/2: # The ampl
itude a = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\n#b
:=2*Pi/p:          # The factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):       \+
   # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis \+
axis = (max+min)/2\nk:=axis:     # k = the distance the reference cosi
ne curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-ma
x(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h
))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\n
if i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(
x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse
\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt
[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[
op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.
01,`Reference function`],\n                        font=[HELVETICA,DEF
AULT,12],\n                        color=red,align=\{BELOW,CENTER\}): \+
\ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n  \+
                      font=[HELVETICA,DEFAULT,12],\n                  \+
      color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([x
right-.01,axis+.09,`axis `],\n                        font=[HELVETICA,
DEFAULT,12],\n                        color=blue,align=\{ABOVE,LEFT\})
:\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue)
:\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=pl
ot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],sty
le=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=poi
nt,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n           [
txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n   \+
         pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n     \+
       #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n
            tickmarks=[9,9],\n            #view=[x_left..x_right,y_ver
tex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n
            title=`Ex.`||Exnum||` Cosine Model:  Reference function sh
ifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  \+
b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List)
;" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%TEXTG6'7
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$$\"3@Zd**Qp**38FXF7FEFfn-FR6%7$F^oF^oFEFfn-FR6&7#F]oFE-%&STYLEG6#%&PO
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FX$!3mG%ob?*G]HFX7$F[`o$!3uoi+5FK1HFX7$Fe`o$!3+IBMvw/yFFX7$F_ao$!3a&*
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EG6$%YEx.5~Cosine~Model:~~Reference~function~shifted~by~[h,~k]G-F:6%F<
F=\"#9-%%VIEWG6$;$!+3`=$G'F)$\"+3`=$G'F);$!\"(F8$\"\"(F8" 1 2 0 1 10 
0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curv
e 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curv
e 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"$/%-~Pe
riod:~~~pG%#PiG/%$~~bG$\"\"#\"\"!/%9~Shift~right~(left):~~~hG,$*(\"\"&
\"\"\"\"#7!\"\"F(F3F3/%6~Shift~up~(down):~~~kGF-" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"$\"\"\"-%$cos
G6#,$*&$\"\"#\"\"!F+F'F+F+F+F+/-%6~Shifted~function:~~fG6#,&F'F+*(\"\"
&F+\"#7!\"\"%#PiGF+F<,$*&F*F+-F-6#,&*&F1F+F'F+F+*&$\"+LLLL$)!#5F+F=F+F
<F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 65 "Ex. 6 Sine & Cosine Models:  Reference fu
nction shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 269 79 "Sine \+
Models:  Reference function shifted by [h, k]:  f(x) = a*sin(b(x - h))
 + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2709 "restart:\nExnum:=6:\nmaxh
t:=2:    # Enter the max value of the graph of the data (a peak)\nminh
t:=-2:   # Enter the min value of the graph of the data (a valley)\np:
=2*Pi:        # Enter the period p = distance between two successive p
eaks (or valleys)\nh:=-3*Pi/4:        # Enter the h = the distance the
 reference sine curve is translated right(left)\nj:=2:        # Enter \+
j = the number of cycles that you want.\nn:=1:        # Enter n = the \+
number of new functions that you want different from sin(x).  \na:=(ma
xht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:             # T
he frequency f = 1/p\n#b:=2*Pi/p:          # The factor b = 2*Pi/p\nb:
=evalf(2*Pi/p,4):          # The factor b = 2*Pi/p\naxis:=(maxht+minht
)/2: # The central axis axis = (max+min)/2\nk:=axis:     # k = the dis
tance the reference sine curve is translated up(down)\nxleft:=-j*p:\nx
right:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,
b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f
(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Re
ference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..y
top,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted funct
ion:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color
=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[text
plot]([xleft/2,ytop-.01,`Reference function`],\n                      \+
  font=[HELVETICA,DEFAULT,12],\n                        color=red,alig
n=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Sh
ifted function`],\n                        font=[HELVETICA,DEFAULT,12]
,\n                        color=blue,align=\{BELOW,CENTER\}):\ntxtp[3
]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n                   \+
     font=[HELVETICA,DEFAULT,12],\n                        color=blue,
align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],li
nestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color
=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp
[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\npointp[2]:=p
lot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=plots[di
splay](\n           [txtp[1],txtp[2],txtp[3],\n            linep[1],li
nep[2],linep[3],\n            pointp[1],pointp[2],\n            seq(pl
t[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n        \+
    labels=[``,``],\n            tickmarks=[9,9],\n            #view=[
x_left..x_right,y_vertex-20..y_vertex+20],\n            titlefont=[HEL
VETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sine Model:  Re
ference function shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,`
 Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down)
:   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 
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7/P)47#y**>Fao7$$\"3AzN4$4tH=\"FX$\"3EY;f\"3Bw*>Fao7$$\"3Sx\"Qq-D$*=\"
FX$\"3WQU&*GpS()>Fao7$$\"3evF)4'pn&>\"FX$\"35)o\"Ro[<p>Fao7$Fa\\o$\"3)
>>(=O/+V>Fao7$F[]o$\"3D)3P$*e#=V<Fao7$Fe]o$\"32PN&zf8UT\"FaoFE-%&TITLE
G6$%WEx.6~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F:6%F<F=
\"#9-%*AXESTICKSG6$FMFM-%+AXESLABELSG6%%!GFdiq-F:6#F=-%%VIEWG6$;$!+iqj
c7F6$\"+iqjc7F6;$!\"&F8$\"\"&F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 
1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG,$*&F%\"\"
\"%#PiGF*F*/%$~~bG$F*\"\"!/%9~Shift~right~(left):~~~hG,$*(\"\"$F*\"\"%
!\"\"F+F*F6/%6~Shift~up~(down):~~~kGF/" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$sinG6#,$*&$F
+\"\"!F+F'F+F+F+F+/-%6~Shifted~function:~~fG6#,&F'F+*(\"\"$F+\"\"%!\"
\"%#PiGF+F+,$*&F*F+-F-6#,&*&F1F+F'F+F+*&$\"+++++v!#5F+F<F+F+F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 270 82 "Cosine Models:  Reference functions shifted by [h, k]:  \+
f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2713 "res
tart:\nExnum:=6:\nmaxht:=2:    # Enter the max value of the graph of t
he data (a peak)\nminht:=-2:   # Enter the min value of the graph of t
he data (a valley)\np:=2*Pi:        # Enter the period p = distance be
tween two successive peaks (or valleys)\nh:=-Pi/4:        # Enter the \+
h = the distance the reference cosine curve is translated right(left)
\nj:=2:        # Enter j = the number of cycles that you want.\nn:=1: \+
       # Enter n = the number of new functions that you want different
 from cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\n
f:=1/p:             # The frequency f = 1/p\n#b:=2*Pi/p:          # Th
e factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):          # The factor b = 2*P
i/p\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/2\nk:=
axis:     # k = the distance the reference cosine curve is translated \+
up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=
max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nfor i
 from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(
a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],
x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):
\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft.
.xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:
\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference function`
],\n                        font=[HELVETICA,DEFAULT,12],\n            \+
            color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textpl
ot]([xright/2,ytop-.01,`Shifted function`],\n                        f
ont=[HELVETICA,DEFAULT,12],\n                        color=blue,align=
\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axi
s `],\n                        font=[HELVETICA,DEFAULT,12],\n         \+
               color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xle
ft,axis],[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k
],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linest
yle=2,color=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,
color=blue):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,color=
blue):\nSinPlot1:=plots[display](\n           [txtp[1],txtp[2],txtp[3]
,\n            linep[1],linep[2],linep[3],\n            pointp[1],poin
tp[2],\n            seq(plt[i],i=0..n)],\n            #labels=[`t (sec
)`,`V (volts)`],\n            labels=[``,``],\n            tickmarks=[
7,9],\n            #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n
            titlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`
||Exnum||` Cosine Model:  Reference function shifted by [h, k]`):\nSin
Plot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (lef
t):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" 
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\"\"&F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curv
e 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curv
e 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplit
ude:~~~aG\"\"#/%-~Period:~~~pG,$*&F%\"\"\"%#PiGF*F*/%$~~bG$F*\"\"!/%9~
Shift~right~(left):~~~hG,$*&\"\"%!\"\"F+F*F5/%6~Shift~up~(down):~~~kGF
/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"x
G,$*&\"\"#\"\"\"-%$cosG6#,$*&$F+\"\"!F+F'F+F+F+F+/-%6~Shifted~function
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{SECT 1 {PARA 3 "" 0 "" {TEXT -1 65 "Ex. 7 Sine & Cosine Models:  Refe
rence function shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 271 
79 "Sine Models:  Reference function shifted by [h, k]:  f(x) = a*sin(
b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2706 "restart:\nExnum:
=7:\nmaxht:=5:    # Enter the max value of the graph of the data (a pe
ak)\nminht:=1:   # Enter the min value of the graph of the data (a val
ley)\np:=Pi/4:        # Enter the period p = distance between two succ
essive peaks (or valleys)\nh:=Pi/16:        # Enter the h = the distan
ce the reference sine curve is translated right(left)\nj:=2:        # \+
Enter j = the number of cycles that you want.\nn:=1:        # Enter n \+
= the number of new functions that you want different from sin(x).  \n
a:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:          \+
   # The frequency f = 1/p\n#b:=2*Pi/p:          # The factor b = 2*Pi
/p\nb:=evalf(2*Pi/p,4):          # The factor b = 2*Pi/p\naxis:=(maxht
+minht)/2: # The central axis axis = (max+min)/2\nk:=axis:     # k = t
he distance the reference sine curve is translated up(down)\nxleft:=-j
*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\n
f:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F
[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i
]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=y
bot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted
 function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop
,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plot
s[textplot]([xleft/2,ytop-.01,`Reference function`],\n                \+
        font=[HELVETICA,DEFAULT,12],\n                        color=re
d,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.
01,`Shifted function`],\n                        font=[HELVETICA,DEFAU
LT,12],\n                        color=blue,align=\{BELOW,CENTER\}):\n
txtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n             \+
           font=[HELVETICA,DEFAULT,12],\n                        color
=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axi
s]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2
,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\n
pointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\npointp
[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=pl
ots[display](\n           [txtp[1],txtp[2],txtp[3],\n            linep
[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n            \+
seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n  \+
          labels=[``,``],\n            tickmarks=[9,9],\n            #
view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            titlefon
t=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sine Mode
l:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   \+
a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up \+
(down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 
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_]o$\"3q3eZ%H*3u5FY7$$\"3[c%ynu)>X:FY$\"3w^?9p()yT5FY7$Fd]o$\"3&y5*z**
)3'=5FY7$$\"3+_h-)zjAc\"FY$\"3U.z3]wl/5FY7$Fi]oFa^oFE-%+AXESLABELSG6%%
!GF^jq-F:6#F=-%*AXESTICKSG6$\"\"*Fdjq-%&TITLEG6$%WEx.7~Sine~Model:~~Re
ference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-%%VIEWG6$;$!+Fjzq:FL$
\"+Fjzq:FL;$!\"(F8$\"\"(F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG,$*&\"\"%!\"\"%#
PiG\"\"\"F-/%$~~bG$\"\")\"\"!/%9~Shift~right~(left):~~~hG,$*&\"#;F+F,F
-F-/%6~Shift~up~(down):~~~kG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/
-%7Reference~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$sinG6#,$*&$\"\")\"
\"!F+F'F+F+F+F+/,&-%6~Shifted~function:~~fG6#,&F'F+*&\"#;!\"\"%#PiGF+F
<F+\"\"$F+,&*&F*F+-F-6#,&*&F1F+F'F+F+*&$\"+++++]!#5F+F=F+F<F+F+F>F+" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 272 82 "Cosine Models:  Reference functions shifted by [h, k]:
  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2711 "r
estart:\nExnum:=7:\nmaxht:=5:    # Enter the max value of the graph of
 the data (a peak)\nminht:=1:   # Enter the min value of the graph of \+
the data (a valley)\np:=Pi/4:        # Enter the period p = distance b
etween two successive peaks (or valleys)\nh:=Pi/8:        # Enter the \+
h = the distance the reference cosine curve is translated right(left)
\nj:=2:        # Enter j = the number of cycles that you want.\nn:=1: \+
       # Enter n = the number of new functions that you want different
 from cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\n
f:=1/p:             # The frequency f = 1/p\n#b:=2*Pi/p:          # Th
e factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):          # The factor b = 2*P
i/p\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/2\nk:=
axis:     # k = the distance the reference cosine curve is translated \+
up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=
max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nfor i
 from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(
a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],
x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):
\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft.
.xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:
\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference function`
],\n                        font=[HELVETICA,DEFAULT,12],\n            \+
            color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textpl
ot]([xright/2,ytop-.01,`Shifted function`],\n                        f
ont=[HELVETICA,DEFAULT,12],\n                        color=blue,align=
\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axi
s `],\n                        font=[HELVETICA,DEFAULT,12],\n         \+
               color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xle
ft,axis],[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k
],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linest
yle=2,color=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,
color=blue):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,color=
blue):\nSinPlot1:=plots[display](\n           [txtp[1],txtp[2],txtp[3]
,\n            linep[1],linep[2],linep[3],\n            pointp[1],poin
tp[2],\n            seq(plt[i],i=0..n)],\n            #labels=[`t (sec
)`,`V (volts)`],\n            labels=[``,``],\n            tickmarks=[
7,9],\n            #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n
            titlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`
||Exnum||` Cosine Model:  Reference function shifted by [h, k]`):\nSin
Plot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (lef
t):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" 
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g;`pS[FY7$F^im$\"39UxVEv27ZFY7$Fcim$\"31)oxO1msc%FY7$Fhim$\"3-?#*QKX=(
R%FY7$F]jm$\"3Q&zA(p_d/UFY7$Fbjm$\"3Q%))eB%Qa#*RFY7$Fgjm$\"37&>90vz&[P
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FY7$Fj\\n$\"3WcCf'*fs9?FY7$F_]n$\"3yzHtaPR!z\"FY7$Fd]n$\"3WWh'**fyye\"
FY7$Fi]n$\"3<\"R24?L3T\"FY7$F^^n$\"3YJpTS3Xi7FY7$Fc^n$\"3o&or$p1T^6FY7
$Fh^n$\"31R2c<X*)p5FY7$F]_n$\"3h&4&[MQjS5FY7$Fb_n$\"3l&Q@#)G/#>5FY7$Fg
_n$\"38+ruF:p05FY7$F\\`n$\"30XTYg&\\,+\"FY7$Fa`n$\"3_<1-\"p+H+\"FY7$Ff
`n$\"3BK,5YGP95FY7$F[an$\"3()\\;dGf^M5FY7$F`an$\"39k@qw>Cj5FY7$Fean$\"
3y8<OoU!f9\"FY7$Fjan$\"3UGQ].u\"4E\"FY7$F_bn$\"3i5vO+pr-9FY7$Fdbn$\"3#
*Q!y)Hz:r:FY7$Fibn$\"3!eiyo,JMw\"FY7$F^cn$\"35ZQk%=Hj(>FY7$Fccn$\"3<'e
$z&yWu@#FY7$Fhcn$\"3!>G_N;kGZ#FY7$F]dn$\"36p'ymo=zt#FY7$Fbdn$\"3=,I))4
Ow2IFY7$Fgdn$\"3kaVP`'zvE$FY7$F\\en$\"3[kic1%eG_$FY7$Faen$\"35^F'G;r#p
PFY7$Ffen$\"3)HHfWbRE+%FY7$F[fn$\"3<RT&)*yzOA%FY7$F`fn$\"3xOOa*Q@IU%FY
7$Fefn$\"3!G+r>dHrf%FY7$Fjfn$\"3.=Cm,q\"Hu%FY7$F_gn$\"3gTUB-,)p&[FY7$F
dgn$\"3(=@Ox)plQ\\FY7$Fign$\"3+[\"e>k#)o'\\FY7$F^hn$\"3w+73#>Bl)\\FY7$
Fchn$\"3mZb[5H\\(*\\FY7$Fhhn$\"3'H)*Qi\"Ru**\\FY7$F]in$\"3/#==)fl6%*\\
FY7$Fbin$\"314kL5%R6)\\FY7$Fgin$\"3kv)y\")Hg3'\\FY7$F\\jn$\"3>&)*eo'RN
L\\FY7$Fajn$\"3=YoLN94d[FY7$Ffjn$\"3Uxx*[6vMv%FY7$F[[o$\"3EO#4ixkIg%FY
7$F`[o$\"3K\")>v(3];U%FY7$Fe[o$\"3(yr\"[J(RF@%FY7$Fj[o$\"3gJA/uTP!)RFY
7$F_\\o$\"3+*\\@/gPjv$FY7$Fd\\o$\"3k+^4%=&f?NFY7$Fi\\o$\"3q7f?7bzwKFY7
$F^]o$\"3+'\\,T(=rGIFY7$Fc]o$\"33oasnr!Qw#FY7$Fh]o$\"3+:yFot0.DFY7$F]^
o$\"35N@Lo$\\5D#FY7$Fb^o$\"3%[OI?G;A,#FY7$Fg^o$\"3GS9szR%)*z\"FY7$F\\_
o$\"3=w5(4v9og\"FY7$Fa_o$\"3jL)GMnRiV\"FY7$Ff_o$\"3IU[@Gz'3H\"FY7$F[`o
$\"3Y(o/`v3a;\"FY7$F``o$\"3q3eZ%H*3u5FY7$Fe`o$\"3w^?9p()yT5FY7$Fj`o$\"
3&y5*z**)3'=5FY7$F_ao$\"3U.z3]wl/5FY7$FdaoFjaoFE-%&TITLEG6$%YEx.7~Cosi
ne~Model:~~Reference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-%*AXESTI
CKSG6$\"\"(\"\"*-%+AXESLABELSG6%%!GFciq-F:6#F=-%%VIEWG6$;$!+Fjzq:FL$\"
+Fjzq:FL;$!\"(F8$F^iqF8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG,$*&\"\"%!\"\"%#
PiG\"\"\"F-/%$~~bG$\"\")\"\"!/%9~Shift~right~(left):~~~hG,$*&F1F+F,F-F
-/%6~Shift~up~(down):~~~kG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%
7Reference~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$cosG6#,$*&$\"\")\"\"!
F+F'F+F+F+F+/,&-%6~Shifted~function:~~fG6#,&F'F+*&F2!\"\"%#PiGF+F;F+\"
\"$F+,&*&F*F+-F-6#,&*&F1F+F'F+F+*&$\"+++++5!\"*F+F<F+F;F+F+F=F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 65 "Ex. 8 Sine & Cosine Models:  Reference function shifted
 by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 273 79 "Sine Models:  Refer
ence function shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 2704 "restart:\nExnum:=8:\nmaxht:=4:    # Ent
er the max value of the graph of the data (a peak)\nminht:=-1:   # Ent
er the min value of the graph of the data (a valley)\np:=Pi:        # \+
Enter the period p = distance between two successive peaks (or valleys
)\nh:=Pi/4:        # Enter the h = the distance the reference sine cur
ve is translated right(left)\nj:=2:        # Enter j = the number of c
ycles that you want.\nn:=1:        # Enter n = the number of new funct
ions that you want different from sin(x).  \na:=(maxht-minht)/2: # The
 amplitude a = (max-min)/2\nf:=1/p:             # The frequency f = 1/
p\n#b:=2*Pi/p:          # The factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):  \+
        # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central \+
axis axis = (max+min)/2\nk:=axis:     # k = the distance the reference
 sine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=
-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*sin(b*(
x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x)
:\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  \+
f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nel
se\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\np
lt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:
=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop
-.01,`Reference function`],\n                        font=[HELVETICA,D
EFAULT,12],\n                        color=red,align=\{BELOW,CENTER\})
: \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n
                        font=[HELVETICA,DEFAULT,12],\n                \+
        color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot](
[xright-.01,axis+.09,`axis `],\n                        font=[HELVETIC
A,DEFAULT,12],\n                        color=blue,align=\{ABOVE,LEFT
\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=bl
ue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:
=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],
style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=
point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n         \+
  [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n
            pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n  \+
          #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``]
,\n            tickmarks=[9,9],\n            #view=[x_left..x_right,y_
vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14]
,\n            title=`Ex.`||Exnum||` Sine Model:  Reference function s
hifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,` \+
 b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List
);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%TEXTG6'
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$%WEx.8~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F96%F;F<\"#
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+++lF)$\"+++++lF)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG#\"\"&\"\"#/%-~Period:~~~pG%#PiG/%$~~
bG$F'\"\"!/%9~Shift~right~(left):~~~hG,$*&\"\"%!\"\"F*\"\"\"F5/%6~Shif
t~up~(down):~~~kG#\"\"$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Refer
ence~function:~~fG6#%\"xG,$*&#\"\"&\"\"#\"\"\"-%$sinG6#,$*&$F,\"\"!F-F
'F-F-F-F-/,&-%6~Shifted~function:~~fG6#,&F'F-*&\"\"%!\"\"%#PiGF-F=F-#
\"\"$F,F-,&*&F*F--F/6#,&*&F3F-F'F-F-*&$\"+++++]!#5F-F>F-F=F-F-F?F-" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 274 82 "Cosine Models:  Reference functions shifted by [h, k]:  \+
f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2710 "res
tart:\nExnum:=8:\nmaxht:=4:    # Enter the max value of the graph of t
he data (a peak)\nminht:=-1:   # Enter the min value of the graph of t
he data (a valley)\np:=Pi:        # Enter the period p = distance betw
een two successive peaks (or valleys)\nh:=Pi/2:        # Enter the h =
 the distance the reference cosine curve is translated right(left)\nj:
=2:        # Enter j = the number of cycles that you want.\nn:=1:     \+
   # Enter n = the number of new functions that you want different fro
m cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=1
/p:             # The frequency f = 1/p\n#b:=2*Pi/p:          # The fa
ctor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):          # The factor b = 2*Pi/p
\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/2\nk:=axi
s:     # k = the distance the reference cosine curve is translated up(
down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max
(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nfor i fr
om 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b
,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=x
left..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFt
xt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xri
ght,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod
:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference function`],\n
                        font=[HELVETICA,DEFAULT,12],\n                \+
        color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot](
[xright/2,ytop-.01,`Shifted function`],\n                        font=
[HELVETICA,DEFAULT,12],\n                        color=blue,align=\{BE
LOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `]
,\n                        font=[HELVETICA,DEFAULT,12],\n             \+
           color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,a
xis],[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h
,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=
2,color=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,colo
r=blue):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue
):\nSinPlot1:=plots[display](\n           [txtp[1],txtp[2],txtp[3],\n \+
           linep[1],linep[2],linep[3],\n            pointp[1],pointp[2
],\n            seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`
V (volts)`],\n            labels=[``,``],\n            tickmarks=[7,9]
,\n            #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n    \+
        titlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Ex
num||` Cosine Model:  Reference function shifted by [h, k]`):\nSinPlot
1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (left): \+
  h`=h,` Shift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" 
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\"3#*o16Qh'o*RFW7$Ffhn$\"3wEvH&*)z'**RFW7$F[in$\"3%G$pw*pXE*RFW7$F`in$
\"3y'35HECk(RFW7$Fein$\"3]>&3FPv5&RFW7$Fjin$\"3Q/SbeCp;RFW7$F_jn$\"3*G
4UTHk8#QFW7$Fdjn$\"3[FUe$*Q%=p$FW7$Fijn$\"3U^O@q4$Q]$FW7$F^[o$\"3ofGj4
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aW#FW7$Fb\\o$\"3w;k.!)Ru]@FW7$Fg\\o$\"3?H=<!R%*f%=FW7$F\\]o$\"3N\"\\RD
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\"[T#F_t7$F__o$!39i&HF3/qa%F_t7$Fd_o$!3e67\"y*3:kjF_t7$Fi_o$!3<9m2f0RK
zF_t7$F^`o$!3;%=;$>Q)Q2*F_t7$Fc`o$!3kzV#fQSwZ*F_t7$Fh`o$!3Apdk_()Qn(*F
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Reference~function~shifted~by~[h,~k]G-F96%F;F<\"#9-%+AXESLABELSG6%%!GF
]iq-F96#F<-%*AXESTICKSG6$\"\"(\"\"*-%%VIEWG6$;$!+3`=$G'F)$\"+3`=$G'F);
$!+++++lF)$\"+++++lF)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG#\"\"&\"\"#/%-~Period:~~~pG%#PiG/%$~~
bG$F'\"\"!/%9~Shift~right~(left):~~~hG,$*&F'!\"\"F*\"\"\"F4/%6~Shift~u
p~(down):~~~kG#\"\"$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Referenc
e~function:~~fG6#%\"xG,$*&#\"\"&\"\"#\"\"\"-%$cosG6#,$*&$F,\"\"!F-F'F-
F-F-F-/,&-%6~Shifted~function:~~fG6#,&F'F-*&F,!\"\"%#PiGF-F<F-#\"\"$F,
F-,&*&F*F--F/6#,&*&F3F-F'F-F-*&$\"+++++5!\"*F-F=F-F<F-F-F>F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 65 "Ex. 9 Sine & Cosine Models:  Reference function shifted
 by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 275 79 "Sine Models:  Refer
ence function shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 2647 "restart:\nExnum:=9:\nmaxht:=8:    # Ent
er the max value of the graph of the data (a peak)\nminht:=-2:   # Ent
er the min value of the graph of the data (a valley)\np:=Pi:        # \+
Enter the period p = distance between two successive peaks (or valleys
)\nh:=0:        # Enter the h = the distance the reference sine curve \+
is translated right(left)\nj:=2:        # Enter j = the number of cycl
es that you want.\nn:=1:        # Enter n = the number of new function
s that you want different from sin(x).  \na:=(maxht-minht)/2: # The am
plitude a = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\n
b:=2*Pi/p:          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # \+
The central axis axis = (max+min)/2\nk:=axis:     # k = the distance t
he reference sine curve is translated up(down)\nxleft:=-j*p:\nxright:=
j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x
)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*
b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference
 function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,col
or=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f
`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):
\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([
xleft/2,ytop-.01,`Reference function`],\n                        font=
[HELVETICA,DEFAULT,12],\n                        color=red,align=\{BEL
OW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted f
unction`],\n                        font=[HELVETICA,DEFAULT,12],\n    \+
                    color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plot
s[textplot]([xright-.01,axis+.09,`axis `],\n                        fo
nt=[HELVETICA,DEFAULT,12],\n                        color=blue,align=
\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyl
e=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue)
:\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=p
lot([[0,0]],style=point,symbol=circle,color=blue):\npointp[2]:=plot([[
h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=plots[display]
(\n           [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2]
,linep[3],\n            pointp[1],pointp[2],\n            seq(plt[i],i
=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n            la
bels=[``,``],\n            tickmarks=[9,9],\n            #view=[x_left
..x_right,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA
,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sine Model:  Referenc
e function shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Perio
d:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`
=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "
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3M>a()>i^>BFX7$Fd]o$\"3uMTSu)*****HFXFE-%&TITLEG6$%WEx.9~Sine~Model:~~
Reference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-%*AXESTICKSG6$\"\"*
F^cq-%+AXESLABELSG6%%!GFbcq-F:6#F=-%%VIEWG6$;$!+3`=$G'F)$\"+3`=$G'F);$
!#8F8$\"#8F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 
"Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" 
"Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/A
mplitude:~~~aG\"\"&/%-~Period:~~~pG%#PiG/%$~~bG\"\"#/%9~Shift~right~(l
eft):~~~hG\"\"!/%6~Shift~up~(down):~~~kG\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"&\"\"\"-%$sin
G6#,$*&\"\"#F+F'F+F+F+F+/,&-%6~Shifted~function:~~fGF&F+\"\"$F+,&*&F*F
+F,F+F+F6F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 276 82 "Cosine Models:  Reference functions shif
ted by [h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2656 "restart:\nExnum:=9:\nmaxht:=8:    # Enter the max v
alue of the graph of the data (a peak)\nminht:=-2:   # Enter the min v
alue of the graph of the data (a valley)\np:=Pi:        # Enter the pe
riod p = distance between two successive peaks (or valleys)\nh:=Pi/4: \+
       # Enter the h = the distance the reference cosine curve is tran
slated right(left)\nj:=2:        # Enter j = the number of cycles that
 you want.\nn:=1:        # Enter n = the number of new functions that \+
you want different from cos(x).  \na:=(maxht-minht)/2: # The amplitude
 a = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi
/p:          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The cen
tral axis axis = (max+min)/2\nk:=axis:     # k = the distance the refe
rence cosine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:
\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a
*cos(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*
h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference fun
ction:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=r
ed):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-
h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi
:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xlef
t/2,ytop-.01,`Reference function`],\n                        font=[HEL
VETICA,DEFAULT,12],\n                        color=red,align=\{BELOW,C
ENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted funct
ion`],\n                        font=[HELVETICA,DEFAULT,12],\n        \+
                color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[te
xtplot]([xright-.01,axis+.09,`axis `],\n                        font=[
HELVETICA,DEFAULT,12],\n                        color=blue,align=\{ABO
VE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,c
olor=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nli
nep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([
[0,0]],style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]]
,style=point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n  \+
         [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],line
p[3],\n            pointp[1],pointp[2],\n            seq(plt[i],i=0..n
)],\n            #labels=[`t (sec)`,`V (volts)`],\n            labels=
[``,``],\n            tickmarks=[7,9],\n            #view=[x_left..x_r
ight,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEFA
ULT,14],\n            title=`Ex.`||Exnum||` Cosine Model:  Reference f
unction shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period: \+
  p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k;
\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-
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{PARA 3 "" 0 "" {TEXT -1 66 "Ex. 10 Sine & Cosine Models:  Reference f
unction shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 277 79 "Sine
 Models:  Reference function shifted by [h, k]:  f(x) = a*sin(b(x - h)
) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2648 "restart:\nExnum:=10:\nma
xht:=0:    # Enter the max value of the graph of the data (a peak)\nmi
nht:=-4:   # Enter the min value of the graph of the data (a valley)\n
p:=4:        # Enter the period p = distance between two successive pe
aks (or valleys)\nh:=-1:        # Enter the h = the distance the refer
ence sine curve is translated right(left)\nj:=2:        # Enter j = th
e number of cycles that you want.\nn:=1:        # Enter n = the number
 of new functions that you want different from sin(x).  \na:=(maxht-mi
nht)/2: # The amplitude a = (max-min)/2\nf:=1/p:             # The fre
quency f = 1/p\nb:=2*Pi/p:          # The factor b = 2*Pi/p\naxis:=(ma
xht+minht)/2: # The central axis axis = (max+min)/2\nk:=axis:     # k \+
= the distance the reference sine curve is translated up(down)\nxleft:
=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k)
:\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do
\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFt
xt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright
,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shi
fted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..
ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=
plots[textplot]([xleft/2,ytop-.01,`Reference function`],\n            \+
            font=[HELVETICA,DEFAULT,12],\n                        colo
r=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,yt
op-.01,`Shifted function`],\n                        font=[HELVETICA,D
EFAULT,12],\n                        color=blue,align=\{BELOW,CENTER\}
):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n         \+
               font=[HELVETICA,DEFAULT,12],\n                        c
olor=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright
,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linesty
le=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue
):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\npo
intp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1
:=plots[display](\n           [txtp[1],txtp[2],txtp[3],\n            l
inep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n        \+
    seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],
\n            labels=[``,``],\n            tickmarks=[9,9],\n         \+
   #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            titl
efont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sine \+
Model:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amplitude
:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift
 up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 
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>I9F_q7$Fgdn$\"3u6]JB.IMhFiw7$$\"3yKL3nj)R)eF\\q$\"30I>[L^t6LFiw7$F\\e
n$\"3'*[5!*f.oZ8Fiw7$$\"3%****\\7f?\"ofF\\q$\"3)HZqaj(32DF\\`l7$Faen$
\"3YiEUfO%3c#Fd^p7$$\"3QmmT5I%)[gF\\q$\"3EsG$z4VM)eF\\`l7$Ffen$\"3u\")
o&4\\fg)=Fiw7$$\"3,LLeCO:EhF\\q$\"3s&*foS4(R\"RFiw7$F[fn$\"3OMzu1VgkmF
iw7$F`fn$\"3k1yP#z&3H9F_q7$Fefn$\"3wKt>U!\\_Y#F_q7$Fjfn$\"31NK\"*yCNpR
F_q7$F_gn$\"3Y_X*)4%*\\$y&F_q7$Fdgn$\"3!)oja9IgsyF_q7$Fign$\"3d'zXD'ei
>5F\\q7$F^hn$\"3-l(**)QCmV7F\\q7$Fchn$\"3GHwRd[Sz9F\\q7$F]in$\"3#RK[3`
/Ks\"F\\q7$Fgin$\"3)>.l)p\")Gr>F\\q7$Fajn$\"38ZcYwG>OAF\\q7$F[[o$\"3![
*QMvE%p\\#F\\q7$F`[o$\"33jy\"Rn]*[FF\\q7$Fe[o$\"3Y@?0ePy()HF\\q7$$\"3P
+++Dws4uF\\q$\"3[a.cdg:+KF\\q7$Fj[o$\"3A->$GG&=$R$F\\q7$$\"3O+++&Hy9d(
F\\q$\"3uG2Ec.wjNF\\q7$F_\\o$\"3R8?y'4K\"4PF\\q7$Fd\\o$\"3Aw$zSE\"fMQF
\\q7$Fi\\o$\"3fb#)z=2\"f#RF\\q7$$\"37++D6EjpyF\\q$\"3[dN#4C6#eRF\\q7$F
^]o$\"3/dY(p5\"R\")RF\\q7$$\"3/++v.UaczF\\q$\"3!z_DLNU`*RF\\q7$FYFAFD-
%&TITLEG6$%WEx.1~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F9
6%F;F<\"#9-%*AXESTICKSG6$\"\"*F]jq-%+AXESLABELSG6%%!GFajq-F96#F<-%%VIE
WG6$;FUFY;$!\"'F)$\"\"'F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG\"\"%/%$~~bG,$*&
F%!\"\"%#PiG\"\"\"F//%9~Shift~right~(left):~~~hGF-/%6~Shift~up~(down):
~~~kGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG
6#%\"xG,$*&\"\"#\"\"\"-%$sinG6#,$*(F*!\"\"%#PiGF+F'F+F+F+F+/,&-%6~Shif
ted~function:~~fG6#,&F'F+F+F+F+F*F+,&*&F*F+-F-6#,$*(F*F1F2F+F8F+F+F+F+
F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT 278 82 "Cosine Models:  Reference functions shifted by [
h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
2656 "restart:\nExnum:=10:\nmaxht:=0:    # Enter the max value of the \+
graph of the data (a peak)\nminht:=-4:   # Enter the min value of the \+
graph of the data (a valley)\np:=4*Pi:        # Enter the period p = d
istance between two successive peaks (or valleys)\nh:=0:        # Ente
r the h = the distance the reference cosine curve is translated right(
left)\nj:=2:        # Enter j = the number of cycles that you want.\nn
:=1:        # Enter n = the number of new functions that you want diff
erent from cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min
)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p:          \+
# The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axi
s = (max+min)/2\nk:=axis:     # k = the distance the reference cosine \+
curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2
*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+
k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif \+
i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):
\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[
i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:
=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(L
ist),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`
Reference function`],\n                        font=[HELVETICA,DEFAULT
,12],\n                        color=red,align=\{BELOW,CENTER\}): \ntx
tp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n      \+
                  font=[HELVETICA,DEFAULT,12],\n                      \+
  color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xrigh
t-.01,axis+.09,`axis `],\n                        font=[HELVETICA,DEFA
ULT,12],\n                        color=blue,align=\{ABOVE,LEFT\}):\nl
inep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nl
inep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([
[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=p
oint,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=point,s
ymbol=circle,color=blue):\nSinPlot1:=plots[display](\n           [txtp
[1],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n       \+
     pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n         \+
   #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n    \+
        tickmarks=[7,9],\n            #view=[x_left..x_right,y_vertex-
20..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n    \+
        title=`Ex.`||Exnum||` Cosine Model:  Reference function shifte
d by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b
,` Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }
}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%TEXTG6'7$$!+
iqjc7!\")$\"$*\\!\"#Q3Reference~function6\"%+ALIGNBELOWG-%'COLOURG6&%$
RGBG$\"*++++\"F)$\"\"!F7F6-%%FONTG6%%*HELVETICAG%(DEFAULTG\"#7-F$6'7$$
\"+iqjc7F)F*Q1Shifted~functionF.F/-F16&F3F6F6F4F8-F$6(7$$\"+BTF7DF)$!$
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%&POINTG-FQ6&7#F]oFDFeoFio-FQ6$7[x7$$!3<++&y6uK^#FW$\"3M**************
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3'yDRo'RNLRFhp7$F[jn$!3o#)yIN94dQFhp7$F`jn$!39&yf[6vMv$Fhp7$Fejn$!3eU8
;wZ1.OFhp7$Fjjn$!3Bl[p(3];U$Fhp7$F_[o$!3XkiTJ(RF@$Fhp7$Fd[o$!3aB&pR<u.
)HFhp7$Fi[o$!3ubLM+wLcFFhp7$F^\\o$!3PWE,%=&f?DFhp7$Fc\\o$!3qc.77bzwAFh
p7$Fh\\o$!3zAT,u=rG?Fhp7$F]]o$!37Ywjnr!Qw\"Fhp7$Fb]o$!3XD6>ot0.:Fhp7$F
g]o$!3[s\"[#o$\\5D\"Fhp7$F\\^o$!3o22&>G;A,\"Fhp7$Fa^o$!3YvMZ'zR%)*zFfs
7$Ff^o$!3!e)*Q!4v9ogFfs7$F[_o$!3g@$)pLnRiVFfs7$F`_o$!3,c;l\"Gz'3HFfs7$
Fe_o$!3U\\;m_v3a;Ffs7$Fj_o$!3nYG%\\WH*3uFft7$F_`o$!3Cl[?7p()yTFft7$Fd`
o$!3#\\fk&y**)3'=Fft7$Fi`o$!3=8&>63]wl%Fc]l7$F^aoFdaoFD-%&TITLEG6$%ZEx
.10~Cosine~Model:~~Reference~function~shifted~by~[h,~k]G-F96%F;F<\"#9-
%*AXESTICKSG6$\"\"(\"\"*-%+AXESLABELSG6%%!GF`iq-F96#F<-%%VIEWG6$;$!+BT
F8DF)$\"+BTF8DF);$!\"&F7$\"\"&F7" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 
1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG,$*&\"\"%\"
\"\"%#PiGF+F+/%$~~bG#F+F%/%9~Shift~right~(left):~~~hG\"\"!/%6~Shift~up
~(down):~~~kG!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~fun
ction:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$cosG6#,$*&F*!\"\"F'F+F+F+F+/,&-%6~S
hifted~function:~~fGF&F+F*F1,&*&F*F+F,F+F+F*F1" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 66 "Ex. \+
11 Sine & Cosine Models:  Reference function shifted by [h, k]" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 279 79 "Sine Models:  Reference function \+
shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2708 "restart:\nExnum:=11:\nmaxht:=3:    # Enter the max \+
value of the graph of the data (a peak)\nminht:=-3:   # Enter the min \+
value of the graph of the data (a valley)\np:=2*Pi:        # Enter the
 period p = distance between two successive peaks (or valleys)\nh:=Pi/
6:        # Enter the h = the distance the reference sine curve is tra
nslated right(left)\nj:=2:        # Enter j = the number of cycles tha
t you want.\nn:=1:        # Enter n = the number of new functions that
 you want different from sin(x).  \na:=(maxht-minht)/2: # The amplitud
e a = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\n#b:=2*
Pi/p:          # The factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):          #
 The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis
 = (max+min)/2\nk:=axis:     # k = the distance the reference sine cur
ve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+
1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->-a*sin(b*(x-h))+k:
\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i \+
= 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\n
plt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]
:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=p
lot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(Lis
t),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Re
ference function`],\n                        font=[HELVETICA,DEFAULT,1
2],\n                        color=red,align=\{BELOW,CENTER\}): \ntxtp
[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n        \+
                font=[HELVETICA,DEFAULT,12],\n                        \+
color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-
.01,axis+.09,`axis `],\n                        font=[HELVETICA,DEFAUL
T,12],\n                        color=blue,align=\{ABOVE,LEFT\}):\nlin
ep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlin
ep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h
,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=poi
nt,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=point,sym
bol=circle,color=blue):\nSinPlot1:=plots[display](\n           [txtp[1
],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n         \+
   pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n           \+
 #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n      \+
      tickmarks=[9,9],\n            #view=[x_left..x_right,y_vertex-20
..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n      \+
      title=`Ex.`||Exnum||` Sine Model:  Reference function shifted by
 [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` S
hift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}
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Ex.11~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-
%%VIEWG6$;$!+iqjc7F6$\"+iqjc7F6;$!\"(F8$\"\"(F8" 1 2 0 1 10 0 2 9 1 4 
2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curv
e 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}
{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"$/%-~Period:~~~p
G,$*&\"\"#\"\"\"%#PiGF+F+/%$~~bG$F+\"\"!/%9~Shift~right~(left):~~~hG,$
*&\"\"'!\"\"F,F+F+/%6~Shift~up~(down):~~~kGF0" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"$\"\"\"-%$sin
G6#,$*&$F+\"\"!F+F'F+F+F+!\"\"/-%6~Shifted~function:~~fG6#,&F'F+*&\"\"
'F3%#PiGF+F3,$*&F*F+-F-6#,&*&F1F+F'F+F+*&$\"+nmmm;!#5F+F;F+F3F+F3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 280 82 "Cosine Models:  Reference functions shifted by [h, k]:  \+
f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2651 "res
tart:\nExnum:=1:\nmaxht:=4:    # Enter the max value of the graph of t
he data (a peak)\nminht:=0:   # Enter the min value of the graph of th
e data (a valley)\np:=4:        # Enter the period p = distance betwee
n two successive peaks (or valleys)\nh:=0:        # Enter the h = the \+
distance the reference cosine curve is translated right(left)\nj:=2:  \+
      # Enter j = the number of cycles that you want.\nn:=1:        # \+
Enter n = the number of new functions that you want different from cos
(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:  \+
           # The frequency f = 1/p\nb:=2*Pi/p:          # The factor b
 = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/
2\nk:=axis:     # k = the distance the reference cosine curve is trans
lated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\n
ytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:
\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF
[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plo
t(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h
,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=
xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=
F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference fun
ction`],\n                        font=[HELVETICA,DEFAULT,12],\n      \+
                  color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[
textplot]([xright/2,ytop-.01,`Shifted function`],\n                   \+
     font=[HELVETICA,DEFAULT,12],\n                        color=blue,
align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.0
9,`axis `],\n                        font=[HELVETICA,DEFAULT,12],\n   \+
                     color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot
([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot
([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],
linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=c
ircle,color=blue):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,
color=blue):\nSinPlot1:=plots[display](\n           [txtp[1],txtp[2],t
xtp[3],\n            linep[1],linep[2],linep[3],\n            pointp[1
],pointp[2],\n            seq(plt[i],i=0..n)],\n            #labels=[`
t (sec)`,`V (volts)`],\n            labels=[``,``],\n            tickm
arks=[7,9],\n            #view=[x_left..x_right,y_vertex-20..y_vertex+
20],\n            titlefont=[HELVETICA,DEFAULT,14],\n            title
=`Ex.`||Exnum||` Cosine Model:  Reference function shifted by [h, k]`)
:\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift righ
t (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 
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2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve
 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve
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{XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$cos
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{SECT 1 {PARA 3 "" 0 "" {TEXT -1 66 "Ex. 12 Sine & Cosine Models:  Ref
erence function shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 281 
79 "Sine Models:  Reference function shifted by [h, k]:  f(x) = a*sin(
b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2647 "restart:\nExnum:
=12:\nmaxht:=4:    # Enter the max value of the graph of the data (a p
eak)\nminht:=0:   # Enter the min value of the graph of the data (a va
lley)\np:=4:        # Enter the period p = distance between two succes
sive peaks (or valleys)\nh:=-1:        # Enter the h = the distance th
e reference sine curve is translated right(left)\nj:=2:        # Enter
 j = the number of cycles that you want.\nn:=1:        # Enter n = the
 number of new functions that you want different from sin(x).  \na:=(m
axht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p:             # \+
The frequency f = 1/p\nb:=2*Pi/p:          # The factor b = 2*Pi/p\nax
is:=(maxht+minht)/2: # The central axis axis = (max+min)/2\nk:=axis:  \+
   # k = the distance the reference sine curve is translated up(down)
\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+
1,2*a+k):\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 \+
to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,
x):\nFtxt[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft.
.xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]
:=` Shifted function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y
=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntx
tp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference function`],\n     \+
                   font=[HELVETICA,DEFAULT,12],\n                     \+
   color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xrig
ht/2,ytop-.01,`Shifted function`],\n                        font=[HELV
ETICA,DEFAULT,12],\n                        color=blue,align=\{BELOW,C
ENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n  \+
                      font=[HELVETICA,DEFAULT,12],\n                  \+
      color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],
[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],
linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,col
or=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blu
e):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nS
inPlot1:=plots[display](\n           [txtp[1],txtp[2],txtp[3],\n      \+
      linep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n \+
           seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (vo
lts)`],\n            labels=[``,``],\n            tickmarks=[9,9],\n  \+
          #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n         \+
   titlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||
` Sine Model:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Am
plitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,
` Shift up (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 
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F96#F<-%%VIEWG6$;FUFY;$!\"'F)$\"\"'F)" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+
4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}
{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~p
G\"\"%/%$~~bG,$*&F%!\"\"%#PiG\"\"\"F//%9~Shift~right~(left):~~~hGF-/%6
~Shift~up~(down):~~~kGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Refere
nce~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$sinG6#,$*(F*!\"\"%#PiGF+F'F+
F+F+F+/,&-%6~Shifted~function:~~fG6#,&F'F+F+F+F+F*F+,&*&F*F+-F-6#,$*(F
*F1F2F+F8F+F+F+F+F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT 282 82 "Cosine Models:  Reference funct
ions shifted by [h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 2655 "restart:\nExnum:=12:\nmaxht:=8:    # Enter the m
ax value of the graph of the data (a peak)\nminht:=0:   # Enter the mi
n value of the graph of the data (a valley)\np:=Pi:        # Enter the
 period p = distance between two successive peaks (or valleys)\nh:=Pi:
        # Enter the h = the distance the reference cosine curve is tra
nslated right(left)\nj:=2:        # Enter j = the number of cycles tha
t you want.\nn:=1:        # Enter n = the number of new functions that
 you want different from cos(x).  \na:=(maxht-minht)/2: # The amplitud
e a = (max-min)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*P
i/p:          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The ce
ntral axis axis = (max+min)/2\nk:=axis:     # k = the distance the ref
erence cosine curve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:
\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->-
a*cos(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i
*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference fu
nction:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=
red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x
-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nf
i:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xle
ft/2,ytop-.01,`Reference function`],\n                        font=[HE
LVETICA,DEFAULT,12],\n                        color=red,align=\{BELOW,
CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted func
tion`],\n                        font=[HELVETICA,DEFAULT,12],\n       \+
                 color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[t
extplot]([xright-.01,axis+.09,`axis `],\n                        font=
[HELVETICA,DEFAULT,12],\n                        color=blue,align=\{AB
OVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,
color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nl
inep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot(
[[0,0]],style=point,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]
],style=point,symbol=circle,color=blue):\nSinPlot1:=plots[display](\n \+
          [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[2],lin
ep[3],\n            pointp[1],pointp[2],\n            seq(plt[i],i=0..
n)],\n            #labels=[`t (sec)`,`V (volts)`],\n            labels
=[``,``],\n            tickmarks=[7,9],\n            #view=[x_left..x_
right,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETICA,DEF
AULT,14],\n            title=`Ex.`||Exnum||` Cosine Model:  Reference \+
function shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:
   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   k`=k
;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60
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3^bG&\\;+`J*Fb`m7$FcaoFiaoFE-%*AXESTICKSG6$\"\"(\"\"*-%&TITLEG6$%ZEx.1
2~Cosine~Model:~~Reference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-%+
AXESLABELSG6%%!GFeiq-F:6#F=-%%VIEWG6$;$!+3`=$G'F)$\"+3`=$G'F);$!#7F8$F
>F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1
" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8
" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude
:~~~aG\"\"%/%-~Period:~~~pG%#PiG/%$~~bG\"\"#/%9~Shift~right~(left):~~~
hGF(/%6~Shift~up~(down):~~~kGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%
7Reference~function:~~fG6#%\"xG,$*&\"\"%\"\"\"-%$cosG6#,$*&\"\"#F+F'F+
F+F+!\"\"/,&-%6~Shifted~function:~~fG6#,&F'F+%#PiGF2F+F*F+,&*&F*F+F,F+
F2F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 66 "Ex. 13 Sine & Cosine Models:  Reference f
unction shifted by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 283 79 "Sine
 Models:  Reference function shifted by [h, k]:  f(x) = a*sin(b(x - h)
) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2646 "restart:\nExnum:=1:\nmax
ht:=4:    # Enter the max value of the graph of the data (a peak)\nmin
ht:=0:   # Enter the min value of the graph of the data (a valley)\np:
=4:        # Enter the period p = distance between two successive peak
s (or valleys)\nh:=-1:        # Enter the h = the distance the referen
ce sine curve is translated right(left)\nj:=2:        # Enter j = the \+
number of cycles that you want.\nn:=1:        # Enter n = the number o
f new functions that you want different from sin(x).  \na:=(maxht-minh
t)/2: # The amplitude a = (max-min)/2\nf:=1/p:             # The frequ
ency f = 1/p\nb:=2*Pi/p:          # The factor b = 2*Pi/p\naxis:=(maxh
t+minht)/2: # The central axis axis = (max+min)/2\nk:=axis:     # k = \+
the distance the reference sine curve is translated up(down)\nxleft:=-
j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):
\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n
#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt
[i]:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y
=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shift
ed function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..yt
op,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=pl
ots[textplot]([xleft/2,ytop-.01,`Reference function`],\n              \+
          font=[HELVETICA,DEFAULT,12],\n                        color=
red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop
-.01,`Shifted function`],\n                        font=[HELVETICA,DEF
AULT,12],\n                        color=blue,align=\{BELOW,CENTER\}):
\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n           \+
             font=[HELVETICA,DEFAULT,12],\n                        col
or=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,a
xis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle
=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):
\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\npoin
tp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=
plots[display](\n           [txtp[1],txtp[2],txtp[3],\n            lin
ep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n          \+
  seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n
            labels=[``,``],\n            tickmarks=[9,9],\n           \+
 #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            titlef
ont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sine Mo
del:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amplitude: \+
  a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift u
p (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 
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F_q7$F_gn$\"3Y_X*)4%*\\$y&F_q7$Fdgn$\"3!)oja9IgsyF_q7$Fign$\"3d'zXD'ei
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+++Dws4uF\\q$\"3[a.cdg:+KF\\q7$Fj[o$\"3A->$GG&=$R$F\\q7$$\"3O+++&Hy9d(
F\\q$\"3uG2Ec.wjNF\\q7$F_\\o$\"3R8?y'4K\"4PF\\q7$Fd\\o$\"3Aw$zSE\"fMQF
\\q7$Fi\\o$\"3fb#)z=2\"f#RF\\q7$$\"37++D6EjpyF\\q$\"3[dN#4C6#eRF\\q7$F
^]o$\"3/dY(p5\"R\")RF\\q7$$\"3/++v.UaczF\\q$\"3!z_DLNU`*RF\\q7$FYFAFD-
%&TITLEG6$%WEx.1~Sine~Model:~~Reference~function~shifted~by~[h,~k]G-F9
6%F;F<\"#9-%*AXESTICKSG6$\"\"*F]jq-%+AXESLABELSG6%%!GFajq-F96#F<-%%VIE
WG6$;FUFY;$!\"'F)$\"\"'F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG\"\"%/%$~~bG,$*&
F%!\"\"%#PiG\"\"\"F//%9~Shift~right~(left):~~~hGF-/%6~Shift~up~(down):
~~~kGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG
6#%\"xG,$*&\"\"#\"\"\"-%$sinG6#,$*(F*!\"\"%#PiGF+F'F+F+F+F+/,&-%6~Shif
ted~function:~~fG6#,&F'F+F+F+F+F*F+,&*&F*F+-F-6#,$*(F*F1F2F+F8F+F+F+F+
F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT 284 82 "Cosine Models:  Reference functions shifted by [
h, k]:  f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
2652 "restart:\nExnum:=13:\nmaxht:=5:    # Enter the max value of the \+
graph of the data (a peak)\nminht:=1:   # Enter the min value of the g
raph of the data (a valley)\np:=4:        # Enter the period p = dista
nce between two successive peaks (or valleys)\nh:=1:        # Enter th
e h = the distance the reference cosine curve is translated right(left
)\nj:=2:        # Enter j = the number of cycles that you want.\nn:=1:
        # Enter n = the number of new functions that you want differen
t from cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2
\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p:          # T
he factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis =
 (max+min)/2\nk:=axis:     # k = the distance the reference cosine cur
ve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+
1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:
\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i \+
= 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\n
plt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]
:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=p
lot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(Lis
t),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Re
ference function`],\n                        font=[HELVETICA,DEFAULT,1
2],\n                        color=red,align=\{BELOW,CENTER\}): \ntxtp
[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n        \+
                font=[HELVETICA,DEFAULT,12],\n                        \+
color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-
.01,axis+.09,`axis `],\n                        font=[HELVETICA,DEFAUL
T,12],\n                        color=blue,align=\{ABOVE,LEFT\}):\nlin
ep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlin
ep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h
,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=poi
nt,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=point,sym
bol=circle,color=blue):\nSinPlot1:=plots[display](\n           [txtp[1
],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n         \+
   pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n           \+
 #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n      \+
      tickmarks=[7,9],\n            #view=[x_left..x_right,y_vertex-20
..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n      \+
      title=`Ex.`||Exnum||` Cosine Model:  Reference function shifted \+
by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,`
 Shift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}
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10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C
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~Period:~~~pG\"\"%/%$~~bG,$*&F%!\"\"%#PiG\"\"\"F//%9~Shift~right~(left
):~~~hGF//%6~Shift~up~(down):~~~kG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$/-%7Reference~function:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$cosG6#,$*(F*
!\"\"%#PiGF+F'F+F+F+F+/,&-%6~Shifted~function:~~fG6#,&F'F+F+F1F+\"\"$F
+,&*&F*F+-F-6#,$*(F*F1F2F+F8F+F+F+F+F9F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 66 "Ex. 14 Sine
 & Cosine Models:  Reference function shifted by [h, k]" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 285 79 "Sine Models:  Reference function shifted
 by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 2648 "restart:\nExnum:=14:\nmaxht:=3:    # Enter the max value of \+
the graph of the data (a peak)\nminht:=-9:   # Enter the min value of \+
the graph of the data (a valley)\np:=8:        # Enter the period p = \+
distance between two successive peaks (or valleys)\nh:=-2:        # En
ter the h = the distance the reference sine curve is translated right(
left)\nj:=2:        # Enter j = the number of cycles that you want.\nn
:=1:        # Enter n = the number of new functions that you want diff
erent from sin(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min
)/2\nf:=1/p:             # The frequency f = 1/p\nb:=2*Pi/p:          \+
# The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axi
s = (max+min)/2\nk:=axis:     # k = the distance the reference sine cu
rve is translated up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a
+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:
\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i \+
= 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\n
plt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]
:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nplt[i]:=p
lot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(Lis
t),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Re
ference function`],\n                        font=[HELVETICA,DEFAULT,1
2],\n                        color=red,align=\{BELOW,CENTER\}): \ntxtp
[2]:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n        \+
                font=[HELVETICA,DEFAULT,12],\n                        \+
color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-
.01,axis+.09,`axis `],\n                        font=[HELVETICA,DEFAUL
T,12],\n                        color=blue,align=\{ABOVE,LEFT\}):\nlin
ep[1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlin
ep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h
,0],[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=poi
nt,symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=point,sym
bol=circle,color=blue):\nSinPlot1:=plots[display](\n           [txtp[1
],txtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n         \+
   pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n           \+
 #labels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n      \+
      tickmarks=[9,9],\n            #view=[x_left..x_right,y_vertex-20
..y_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n      \+
      title=`Ex.`||Exnum||` Sine Model:  Reference function shifted by
 [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` S
hift right (left):   h`=h,` Shift up (down):   k`=k;\nop(List);" }}
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\"*F[jq-%&TITLEG6$%XEx.14~Sine~Model:~~Reference~function~shifted~by~[
h,~k]G-F86%F:F;\"#9-%%VIEWG6$;FTFY;$!#8F)$\"#8F)" 1 2 0 1 10 0 2 9 1 
4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Cu
rve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}
}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"'/%-~Period:~~~
pG\"\")/%$~~bG,$*&\"\"%!\"\"%#PiG\"\"\"F0/%9~Shift~right~(left):~~~hG!
\"#/%6~Shift~up~(down):~~~kG!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-
%7Reference~function:~~fG6#%\"xG,$*&\"\"'\"\"\"-%$sinG6#,$*(\"\"%!\"\"
%#PiGF+F'F+F+F+F+/,&-%6~Shifted~function:~~fG6#,&F'F+\"\"#F+F+\"\"$F2,
&*&F*F+-F-6#,$*(F1F2F3F+F9F+F+F+F+F;F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 286 82 "Cosine Model
s:  Reference functions shifted by [h, k]:  f(x) = a*cos(b(x - h)) + k
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2651 "restart:\nExnum:=1:\nmaxht:=4
:    # Enter the max value of the graph of the data (a peak)\nminht:=0
:   # Enter the min value of the graph of the data (a valley)\np:=4:  \+
      # Enter the period p = distance between two successive peaks (or
 valleys)\nh:=0:        # Enter the h = the distance the reference cos
ine curve is translated right(left)\nj:=2:        # Enter j = the numb
er of cycles that you want.\nn:=1:        # Enter n = the number of ne
w functions that you want different from cos(x).  \na:=(maxht-minht)/2
: # The amplitude a = (max-min)/2\nf:=1/p:             # The frequency
 f = 1/p\nb:=2*Pi/p:          # The factor b = 2*Pi/p\naxis:=(maxht+mi
nht)/2: # The central axis axis = (max+min)/2\nk:=axis:     # k = the \+
distance the reference cosine curve is translated up(down)\nxleft:=-j*
p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf
:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nfor i from 0 to n do\n#F[
i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]
:=`Reference function:  f`(x):\nplt[i]:=plot(F[i],x=xleft..xright,y=yb
ot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted \+
function:  f`(x-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,
color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nod:\ntxtp[1]:=plots
[textplot]([xleft/2,ytop-.01,`Reference function`],\n                 \+
       font=[HELVETICA,DEFAULT,12],\n                        color=red
,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.0
1,`Shifted function`],\n                        font=[HELVETICA,DEFAUL
T,12],\n                        color=blue,align=\{BELOW,CENTER\}):\nt
xtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n              \+
          font=[HELVETICA,DEFAULT,12],\n                        color=
blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis
]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,
color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\np
ointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):\npointp[
2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=plo
ts[display](\n           [txtp[1],txtp[2],txtp[3],\n            linep[
1],linep[2],linep[3],\n            pointp[1],pointp[2],\n            s
eq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n   \+
         labels=[``,``],\n            tickmarks=[7,9],\n            #v
iew=[x_left..x_right,y_vertex-20..y_vertex+20],\n            titlefont
=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Cosine Mod
el:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amplitude:  \+
 a`=a,` Period:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up
 (down):   k`=k;\nop(List);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 
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\"#9-%%VIEWG6$;FUFY;$!\"'F)$\"\"'F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 
1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"\"#/%-~Period:~~~pG\"\"%/%$~~b
G,$*&F%!\"\"%#PiG\"\"\"F//%9~Shift~right~(left):~~~hG\"\"!/%6~Shift~up
~(down):~~~kGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~funct
ion:~~fG6#%\"xG,$*&\"\"#\"\"\"-%$cosG6#,$*(F*!\"\"%#PiGF+F'F+F+F+F+/,&
-%6~Shifted~function:~~fGF&F+F*F+,&*&F*F+F,F+F+F*F+" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 81 
"Ex. 15 Sine & Cosine Models (Tide Problem):  Reference function shift
ed by [h, k]" }}{EXCHG {PARA 0 "" 0 "" {TEXT 258 79 "Sine Models:  Ref
erence function shifted by [h, k]:  f(x) = a*sin(b(x - h)) + k" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2895 "restart:\nExnum:=15:\nmaxht:=58: \+
   # Enter the max value of the graph of the data (a peak)\nminht:=2: \+
  # Enter the min value of the graph of the data (a valley)\np:=6.2:  \+
      # Enter the period p = distance between two successive peaks (or
 valleys)\nh:=0:        # Enter the h = the distance the reference sin
e curve is translated right(left)\nj:=2:        # Enter j = the number
 of cycles that you want.\nn:=1:        # Enter n = the number of new \+
functions that you want different from sin(x).  \na:=(maxht-minht)/2: \+
# The amplitude a = (max-min)/2\nf:=1/p:             # The frequency f
 = 1/p\n#b:=evalf(2/p,4)*Pi:          # The factor b = 2*Pi/p\nb:=eval
f(2*Pi/p,4):          # The factor b = 2*Pi/p\naxis:=(maxht+minht)/2: \+
# The central axis axis = (max+min)/2\nk:=axis:     # k = the distance
 the reference sine curve is translated up(down)\nxleft:=-j*p:\nxright
:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a,b,h,k
,x)->a*sin(b*(x-h))+k:\nList:=[]:\nLList:=[]:\nfor i from 0 to n do\n#
F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[
i]:=`Reference function:  f`(x):\nFF[i]:=f(a,b,0,0,t):\nFFtxt[i]:=`Ref
erence function:  f`(t):\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..yt
op,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted functi
on:  f`(x-h)+k:\nFF[i]:=f(i*a,b,h,k,t):\nFFtxt[i]:=` Shifted function:
  f`(t-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blu
e):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nLList:=[op(LList),FFtxt[i]=F
F[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Reference fun
ction`],\n                        font=[HELVETICA,DEFAULT,12],\n      \+
                  color=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[
textplot]([xright/2,ytop-.01,`Shifted function`],\n                   \+
     font=[HELVETICA,DEFAULT,12],\n                        color=blue,
align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.0
9,`axis `],\n                        font=[HELVETICA,DEFAULT,12],\n   \+
                     color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot
([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlinep[2]:=plot
([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],
linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=point,symbol=c
ircle,color=blue):\npointp[2]:=plot([[h,k]],style=point,symbol=circle,
color=blue):\nSinPlot1:=plots[display](\n           [txtp[1],txtp[2],t
xtp[3],\n            linep[1],linep[2],linep[3],\n            pointp[1
],pointp[2],\n            seq(plt[i],i=0..n)],\n            #labels=[`
t (sec)`,`V (volts)`],\n            labels=[``,``],\n            tickm
arks=[9,9],\n            #view=[x_left..x_right,y_vertex-20..y_vertex+
20],\n            titlefont=[HELVETICA,DEFAULT,14],\n            title
=`Ex.`||Exnum||` Sine Model:  Reference function shifted by [h, k]`):
\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Shift right
 (left):   h`=h,` Shift up (down):   k`=k;\n#op(List);\nop(LList);" }}
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DF^q7$Fijn$\"3e%ehIn#oBHF^q7$F^[o$\"3hAU%\\tll5%F^q7$Fc[o$\"3M9Z+EzYXd
F^q7$Fh[o$\"3K\\B[>qk9xF^q7$F]\\o$\"3&4+uF\\TV+\"FX7$Fb\\o$\"3?&yE]a>%
p7FX7$Fg\\o$\"3+r>9];Ui:FX7$F\\]o$\"3SewbF3,.>FX7$Fa]o$\"3-VqD<s.kAFX7
$Ff]o$\"3\"GE^vzu(QEFX7$Ffn$\"3Yq4Z.@C?IFXFE-%+AXESLABELSG6%%!GFbcq-F:
6#F=-%&TITLEG6$%XEx.15~Sine~Model:~~Reference~function~shifted~by~[h,~
k]G-F:6%F<F=\"#9-%*AXESTICKSG6$\"\"*F_dq-%%VIEWG6$;$!$C\"!\"\"$\"$C\"F
fdq;$!#')F8$\"#')F8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'/%/Amplitude:~~~aG\"#G/%-~Period:~~~pG$\"#i!\"\"/%$~~bG
$\"%95!\"$/%9~Shift~right~(left):~~~hG\"\"!/%6~Shift~up~(down):~~~kG\"
#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"
tG,$*&\"#G\"\"\"-%$sinG6#,$*&$\"%95!\"$F+F'F+F+F+F+/,&-%6~Shifted~func
tion:~~fGF&F+\"#IF+,&*&F*F+F,F+F+F8F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 82 "Cosine Model
s:  Reference functions shifted by [h, k]:  f(x) = a*cos(b(x - h)) + k
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2899 "restart:\nExnum:=15:\nmaxht:=
58:    # Enter the max value of the graph of the data (a peak)\nminht:
=2:   # Enter the min value of the graph of the data (a valley)\np:=12
.4:     # Enter the period p = distance between two successive peaks (
or valleys)\nh:=0:        # Enter the h = the distance the reference c
osine curve is translated right(left)\nj:=2:        # Enter j = the nu
mber of cycles that you want.\nn:=1:        # Enter n = the number of \+
new functions that you want different from cos(x).  \na:=(maxht-minht)
/2: # The amplitude a = (max-min)/2\nf:=1/p:             # The frequen
cy f = 1/p\n#b:=evalf(2/p,4)*Pi:          # The factor b = 2*Pi/p\nb:=
evalf(2*Pi/p,4):          # The factor b = 2*Pi/p\naxis:=(maxht+minht)
/2: # The central axis axis = (max+min)/2\nk:=axis:     # k = the dist
ance the reference cosine curve is translated up(down)\nxleft:=-j*p:\n
xright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nytop:=max(2*a+1,2*a+k):\nf:=(a
,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nLList:=[]:\nfor i from 0 to n
 do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0 then\nF[i]:=f(a,b,0,0,x):
\nFtxt[i]:=`Reference function:  f`(x):\nFF[i]:=f(a,b,0,0,t):\nFFtxt[i
]:=`Reference function:  f`(t):\nplt[i]:=plot(F[i],x=xleft..xright,y=y
bot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h,k,x):\nFtxt[i]:=` Shifted
 function:  f`(x-h)+k:\nFF[i]:=f(i*a,b,h,k,t):\nFFtxt[i]:=` Shifted fu
nction:  f`(t-h)+k:\nplt[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,co
lor=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[i]]:\nLList:=[op(LList),FFt
xt[i]=FF[i]]:\nod:\ntxtp[1]:=plots[textplot]([xleft/2,ytop-.01,`Refere
nce function`],\n                        font=[HELVETICA,DEFAULT,12],
\n                        color=red,align=\{BELOW,CENTER\}): \ntxtp[2]
:=plots[textplot]([xright/2,ytop-.01,`Shifted function`],\n           \+
             font=[HELVETICA,DEFAULT,12],\n                        col
or=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=plots[textplot]([xright-.01
,axis+.09,`axis `],\n                        font=[HELVETICA,DEFAULT,1
2],\n                        color=blue,align=\{ABOVE,LEFT\}):\nlinep[
1]:=plot([[xleft,axis],[xright,axis]],linestyle=2,color=blue):\nlinep[
2]:=plot([[0,k],[h,k]],linestyle=2,color=blue):\nlinep[3]:=plot([[h,0]
,[h,k]],linestyle=2,color=blue):\npointp[1]:=plot([[0,0]],style=point,
symbol=circle,color=blue):\npointp[2]:=plot([[h,k]],style=point,symbol
=circle,color=blue):\nSinPlot1:=plots[display](\n           [txtp[1],t
xtp[2],txtp[3],\n            linep[1],linep[2],linep[3],\n            \+
pointp[1],pointp[2],\n            seq(plt[i],i=0..n)],\n            #l
abels=[`t (sec)`,`V (volts)`],\n            labels=[``,``],\n         \+
   tickmarks=[7,9],\n            #view=[x_left..x_right,y_vertex-20..y
_vertex+20],\n            titlefont=[HELVETICA,DEFAULT,14],\n         \+
   title=`Ex.`||Exnum||` Cosine Model:  Reference function shifted by \+
[h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Period:   p`=p,`  b`=b,` Sh
ift right (left):   h`=h,` Shift up (down):   k`=k;\n#op(List);\nop(LL
ist);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "60-%%TEXT
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&\\FW7$Fe]o$\"3marP\"p3I>&FW7$Fj]o$\"3!yI$3Qf$fR&FW7$F_^o$\"3oE1AG%p3d
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TLEG6$%ZEx.15~Cosine~Model:~~Reference~function~shifted~by~[h,~k]G-F96
%F;F<\"#9-%*AXESTICKSG6$\"\"(\"\"*-%%VIEWG6$;$!$[#!\"\"$\"$[#Fbgq;$!#'
)F7$\"#')F7" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "
Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "
Curve 8" "Curve 9" "Curve 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Am
plitude:~~~aG\"#G/%-~Period:~~~pG$\"$C\"!\"\"/%$~~bG$\"%o]!\"%/%9~Shif
t~right~(left):~~~hG\"\"!/%6~Shift~up~(down):~~~kG\"#I" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$/-%7Reference~function:~~fG6#%\"tG,$*&\"#G\"\"\"-%
$cosG6#,$*&$\"%o]!\"%F+F'F+F+F+F+/,&-%6~Shifted~function:~~fGF&F+\"#IF
+,&*&F*F+F,F+F+F8F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 81 "Ex. 16 Sine & Cosine Models (Tid
e Problem):  Reference function shifted by [h, k]" }}{EXCHG {PARA 0 "
" 0 "" {TEXT 287 79 "Sine Models:  Reference function shifted by [h, k
]:  f(x) = a*sin(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2895 
"restart:\nExnum:=16:\nmaxht:=58:    # Enter the max value of the grap
h of the data (a peak)\nminht:=2:   # Enter the min value of the graph
 of the data (a valley)\np:=6.2:        # Enter the period p = distanc
e between two successive peaks (or valleys)\nh:=0:        # Enter the \+
h = the distance the reference sine curve is translated right(left)\nj
:=2:        # Enter j = the number of cycles that you want.\nn:=1:    \+
    # Enter n = the number of new functions that you want different fr
om sin(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=
1/p:             # The frequency f = 1/p\n#b:=evalf(2/p,4)*Pi:        \+
  # The factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):          # The factor b
 = 2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/
2\nk:=axis:     # k = the distance the reference sine curve is transla
ted up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nyt
op:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*sin(b*(x-h))+k:\nList:=[]:\nL
List:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = \+
0 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nFF
[i]:=f(a,b,0,0,t):\nFFtxt[i]:=`Reference function:  f`(t):\nplt[i]:=pl
ot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,
h,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nFF[i]:=f(i*a,b,h,k,
t):\nFFtxt[i]:=` Shifted function:  f`(t-h)+k:\nplt[i]:=plot(F[i],x=xl
eft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ftxt[i]=F[
i]]:\nLList:=[op(LList),FFtxt[i]=FF[i]]:\nod:\ntxtp[1]:=plots[textplot
]([xleft/2,ytop-.01,`Reference function`],\n                        fo
nt=[HELVETICA,DEFAULT,12],\n                        color=red,align=\{
BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2,ytop-.01,`Shifte
d function`],\n                        font=[HELVETICA,DEFAULT,12],\n \+
                       color=blue,align=\{BELOW,CENTER\}):\ntxtp[3]:=p
lots[textplot]([xright-.01,axis+.09,`axis `],\n                       \+
 font=[HELVETICA,DEFAULT,12],\n                        color=blue,alig
n=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xright,axis]],linest
yle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],linestyle=2,color=blu
e):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=blue):\npointp[1]:
=plot([[0,0]],style=point,symbol=circle,color=blue):\npointp[2]:=plot(
[[h,k]],style=point,symbol=circle,color=blue):\nSinPlot1:=plots[displa
y](\n           [txtp[1],txtp[2],txtp[3],\n            linep[1],linep[
2],linep[3],\n            pointp[1],pointp[2],\n            seq(plt[i]
,i=0..n)],\n            #labels=[`t (sec)`,`V (volts)`],\n            \+
labels=[``,``],\n            tickmarks=[9,9],\n            #view=[x_le
ft..x_right,y_vertex-20..y_vertex+20],\n            titlefont=[HELVETI
CA,DEFAULT,14],\n            title=`Ex.`||Exnum||` Sine Model:  Refere
nce function shifted by [h, k]`):\nSinPlot1;\n`Amplitude:   a`=a,` Per
iod:   p`=p,`  b`=b,` Shift right (left):   h`=h,` Shift up (down):   \+
k`=k;\n#op(List);\nop(LList);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 
486 {PLOTDATA 2 "60-%%TEXTG6'7$$!+++++i!\"*$\"%*f)!\"#Q3Reference~func
tion6\"%+ALIGNBELOWG-%'COLOURG6&%$RGBG$\"*++++\"!\")$\"\"!F8F7-%%FONTG
6%%*HELVETICAG%(DEFAULTG\"#7-F$6'7$$\"+++++iF)F*Q1Shifted~functionF.F/
-F16&F3F7F7F4F9-F$6(7$$\"%R7F,$\"%4IF,Q&axis~F.%*ALIGNLEFTG%+ALIGNABOV
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$\"3hAU%\\tll5%F^q7$Fc[o$\"3M9Z+EzYXdF^q7$Fh[o$\"3K\\B[>qk9xF^q7$F]\\o
$\"3&4+uF\\TV+\"FX7$Fb\\o$\"3?&yE]a>%p7FX7$Fg\\o$\"3+r>9];Ui:FX7$F\\]o
$\"3SewbF3,.>FX7$Fa]o$\"3-VqD<s.kAFX7$Ff]o$\"3\"GE^vzu(QEFX7$Ffn$\"3Yq
4Z.@C?IFXFE-%+AXESLABELSG6%%!GFbcq-F:6#F=-%&TITLEG6$%XEx.16~Sine~Model
:~~Reference~function~shifted~by~[h,~k]G-F:6%F<F=\"#9-%*AXESTICKSG6$\"
\"*F_dq-%%VIEWG6$;$!$C\"!\"\"$\"$C\"Ffdq;$!#')F8$\"#')F8" 1 2 0 1 10 
0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curv
e 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curv
e 10" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG\"#G/%-~Per
iod:~~~pG$\"#i!\"\"/%$~~bG$\"%95!\"$/%9~Shift~right~(left):~~~hG\"\"!/
%6~Shift~up~(down):~~~kG\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%7Re
ference~function:~~fG6#%\"tG,$*&\"#G\"\"\"-%$sinG6#,$*&$\"%95!\"$F+F'F
+F+F+F+/,&-%6~Shifted~function:~~fGF&F+\"#IF+,&*&F*F+F,F+F+F8F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 288 82 "Cosine Models:  Reference functions shifted by [h, k]:  \+
f(x) = a*cos(b(x - h)) + k" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2963 "res
tart:\nExnum:=16:\nmaxht:=4:    # Enter the max value of the graph of \+
the data (a peak)\nminht:=1.8:   # Enter the min value of the graph of
 the data (a valley)\np:=12.8:     # Enter the period p = distance bet
ween two successive peaks (or valleys)\nh:=3:        # Enter the h = t
he distance the reference cosine curve is translated right(left)\nj:=2
:        # Enter j = the number of cycles that you want.\nn:=1:       \+
 # Enter n = the number of new functions that you want different from \+
cos(x).  \na:=(maxht-minht)/2: # The amplitude a = (max-min)/2\nf:=1/p
:             # The frequency f = 1/p\n#b:=evalf(2/p,4)*Pi:          #
 The factor b = 2*Pi/p\nb:=evalf(2*Pi/p,4):          # The factor b = \+
2*Pi/p\naxis:=(maxht+minht)/2: # The central axis axis = (max+min)/2\n
k:=axis:     # k = the distance the reference cosine curve is translat
ed up(down)\nxleft:=-j*p:\nxright:=j*p:\nybot:=-max(2*a+1,2*a+k):\nyto
p:=max(2*a+1,2*a+k):\nf:=(a,b,h,k,x)->a*cos(b*(x-h))+k:\nList:=[]:\nLL
ist:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*h,i*k,x):\nif i = 0
 then\nF[i]:=f(a,b,0,0,x):\nFtxt[i]:=`Reference function:  f`(x):\nFF[
i]:=f(a,b,0,0,t):\nFFtxt[i]:=`Reference function:  f`(t):\nplt[i]:=plo
t(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i*a,b,h
,k,x):\nFtxt[i]:=` Shifted function:  f`(x-h)+k:\nFF[i]:=f(i*a,b,h,k,t
):\nFFtxt[i]:=` Shifted function:  f`(t-h)+evalf(k,4):\nplt[i]:=plot(F
[i],x=xleft..xright,y=ybot..ytop,color=blue):\nfi:\nList:=[op(List),Ft
xt[i]=F[i]]:\nLList:=[op(LList),FFtxt[i]=evalf(FF[i],4)]:\nod:\ntxtp[1
]:=plots[textplot]([xleft/2,ytop-.01,`Reference function`],\n         \+
               font=[HELVETICA,DEFAULT,12],\n                        c
olor=red,align=\{BELOW,CENTER\}): \ntxtp[2]:=plots[textplot]([xright/2
,ytop-.01,`Shifted function`],\n                        font=[HELVETIC
A,DEFAULT,12],\n                        color=blue,align=\{BELOW,CENTE
R\}):\ntxtp[3]:=plots[textplot]([xright-.01,axis+.09,`axis `],\n      \+
                  font=[HELVETICA,DEFAULT,12],\n                      \+
  color=blue,align=\{ABOVE,LEFT\}):\nlinep[1]:=plot([[xleft,axis],[xri
ght,axis]],linestyle=2,color=blue):\nlinep[2]:=plot([[0,k],[h,k]],line
style=2,color=blue):\nlinep[3]:=plot([[h,0],[h,k]],linestyle=2,color=b
lue):\npointp[1]:=plot([[0,0]],style=point,symbol=circle,color=blue):
\npointp[2]:=plot([[h,k]],style=point,symbol=circle,color=blue):\nSinP
lot1:=plots[display](\n           [txtp[1],txtp[2],txtp[3],\n         \+
   linep[1],linep[2],linep[3],\n            pointp[1],pointp[2],\n    \+
        seq(plt[i],i=0..n)],\n            #labels=[`t (sec)`,`V (volts
)`],\n            labels=[``,``],\n            tickmarks=[7,9],\n     \+
       #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n            \+
titlefont=[HELVETICA,DEFAULT,14],\n            title=`Ex.`||Exnum||` C
osine Model:  Reference function shifted by [h, k]`):\nSinPlot1;\n`Amp
litude:   a`=evalf(a,4),` Period:   p`=evalf(p,4),`  b`=evalf(b,4),` S
hift right (left):   h`=evalf(h,4),` Shift up (down):   k`=evalf(k,4);
\n#op(List);\nop(LList);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 
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$!$c#!\"\"$\"$c#Fdiq;$!+++++^F,$\"+++++^F," 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+
4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}}
{PARA 11 "" 1 "" {XPPMATH 20 "6'/%/Amplitude:~~~aG$\"%+6!\"$/%-~Period
:~~~pG$\"$G\"!\"\"/%$~~bG$\"%3\\!\"%/%9~Shift~right~(left):~~~hG$\"\"$
\"\"!/%6~Shift~up~(down):~~~kG$\"%+HF'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$/-%7Reference~function:~~fG6#%\"tG,$*&$\"%+6!\"$\"\"\"-%$cosG6#,
$*&$\"%3\\!\"%F-F'F-F-F-F-/,&-%6~Shifted~function:~~fG6#,&F'F-\"\"$!\"
\"F-$\"%+HF,F-,&*&F*F--F/6#,&*&F3F-F'F-F-$\"%s9F,F=F-F-F>F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "_______________________________
______" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 
"Filename: ExplorePrecalc06Exercises.mws" }}{PARA 0 "" 0 "" {TEXT -1 
36 "Copyright 2005, All Rights Reserved." }}{PARA 0 "" 0 "" {TEXT -1 
44 "Permission is granted to use and modify for " }}{PARA 0 "" 0 "" 
{TEXT -1 37 "academic and non-commercial purposes." }}{PARA 0 "" 0 "" 
{TEXT -1 13 "Dr. John Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "Mathematics
 Department-MICDS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@micds.o
rg or pais@kinetigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL:  http:/
/kinetigram.com/micds" }}{PARA 0 "" 0 "" {TEXT -1 37 "________________
_____________________" }}}{MARK "0 0" 13 }{VIEWOPTS 1 1 0 1 1 1803 1 
1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }