# Finding area in polar coordinates

1. Feb 28, 2007

### raincheck

1. The problem statement, all variables and given/known data
"Find the area of the region described: The region that is enclosed by the rose r=4cos3[theta]"

2. Relevant equations

A= [integral] (1/2)r^2 d[theta]

3. The attempt at a solution

I'll use Q as [theta]..

I'm not really sure, but I set up (1/2) [integral] (16(cos^2)3Q) dQ

.. then I thought we were supposed to use the identity (cos^2)Q = (1/2)(1+cos2Q), but every time I substitute this in and integrate, I get 8[pi] instead of 4[pi], the correct answer. What am I doing wrong?

Thank you so much :]

Last edited: Feb 28, 2007
2. Feb 28, 2007

### ZioX

I get 8pi as well.

3. Feb 28, 2007

### raincheck

hmmm, I asked someone else and they got 8pi too...

Well I had one more question... if I were finding the area between
r = sqrt[cos2(theta)] and
r = 2cos(theta)

do I basically do the same thing as finding the area between two regular curves? Each time I try it, I come up with zeros and I feel like that cant be right :[

4. Mar 1, 2007

### ZioX

That's a really weird graph intersection. Where did you get that question from?

5. Mar 1, 2007

### HallsofIvy

Staff Emeritus
You don't say anything about what limits of integration you used. $\theta$ going from 0 to what traces that figure exactly once?