Selected Homework 11:  Polar Coordinates

Exercise 1.

`a. Create a polar plot of  r = `*f(theta) = 2*sin(theta), ` `*theta = 0 .. 2*Pi

`b. Show that the graph

`c. Find critical points`, dy/dx = 0

`d. Find (polar) arc length.`

`e. Find (polar) area.`

 




 







Exercise 2.

`a. Create a polar plot of  r = `*f(theta) = 2*cos(theta), ` `*theta = 0 .. 2*Pi

`b. Show that the graph

`c. Find critical points`, dy/dx = 0

`d. Find (polar) arc length.`

`e. Find (polar) area.`









Exercise 3.

`a. Create a polar plot of  r = `*f(theta) = tan(theta), ` `*theta = -1/4*Pi .. 1/4*Pi

`b. Show that the graph

`c. Find critical points`, dy/dx = 0

`d. Find (polar) arc length.`

`e. Find (polar) area.`









Exercise 4.

`a. Create a polar plot of  r = `*f(theta) = 1+sin(theta), ` `*theta = 0 .. 2*Pi

`b. Find critical points`, dy/dx = 0

`c. Find (polar) arc length.`

`d. Find (polar) area.`









Exercise 5.

`a. Create a polar plot of  r = `*f(theta) = 1+2*sin(theta), ` `*theta = 0 .. 2*Pi

`b. Find critical points`, dy/dx = 0

`c. Find (polar) arc length.`

`d. Find (polar) area of inner loop.`









Exercise 6.

f(theta) = sin(2*theta)

`a. Create a polar plot of  r = `*f(theta) = sin(2*theta), ` `*theta = 0 .. 2*Pi

`b. Find critical points`, dy/dx = 0

`c. Find (polar) arc length.`

`d. Find (polar) area.`









Exercise 7.

`a. Create a polar plot of  r = `*f(theta) = cos(2*theta), ` `*theta = 0 .. 2*Pi

`b. Find critical points`, dy/dx = 0

`c. Find (polar) arc length.`

`d. Find (polar) area.`









Exercise 8.

`a. Create a polar plot of  r = `*f(theta) = sin(4*theta), ` `*theta = 0 .. 2*Pi

`b. Find critical points`, dy/dx = 0

`c. Find (polar) arc length.`

`d. Find (polar) area.`