What is the graph of a polar curve with specific r and theta values?

[ThirdEyeBlind]

Homework Statement

Sketch a graph of the polar curve whose points satisfy the following:

As theta increases from 0 to pi/2, r decreases from 4 to 2.
As theta increases from pi/2 to pi, r decreases from 2 to 0.
As theta increases from pi to 3pi/2, r decreases from 0 to -1.
As theta increases from 3pi/2 to 2pi, r decreases from -1 to -3.

Homework Equations

The Attempt at a Solution

First, I converted the points from polar to cartesian and got the following:
(r, theta) -> (x,y)
(4, 0) -> (4, 0)
(2, pi/2) -> (0, 2)
(0, pi) -> (0, 0)
(-1, 3pi/2) ->(0, 1)
(-3, 2pi) -> (-3, 0)Then, I graphed the points in order and got:

I think this is right, I am just looking for someone to look over my work as I have to turn this in.

ThanksEdit: Whoops, I meant to post this in the Calculus & Beyond forum. If someone could move it there, I would appreciate it.

 

[vela]

It looks fine to me.

Actually, you might want to refine the curves a bit. Depending on how picky the grader is, he or she might argue that, for instance, r isn't decreasing as you near the point (0,2) from the right.

 

[LCKurtz]

Also, I would suggest that for such problems, there is no need to convert to rectangular coordinates. Just draw lines at a few theta values and mark off r values that satisfy your conditions.