# Thread: Area between two polar equations

1. ## Area between two polar equations

Hi,

I am asked to solve the region R bounded inside of r = 1+cos(4theta) and outside r = 2. Now I know I need to find the points of intersections, by equaling both equations. So I find theta to be pi/32, 3pi/32, etc. First equation is, does it make sense? I mean I have drawn the graph of both:

Hum sorry, picture is rotated counter-clock wise. 0 is at the top. Anyhow, does it make sense that the first point of intersection hits at pi/32? and second, is it a legit move, to take the integral from o to pi/32, and by symmetry, multiply it by 8 to get the area of all the "petals", since my area I blacked is symmetric to the other side.

Thanks,

R.

2. ## Re: Area between two polar equations

Hello, richardsim10!

Is there a typo? .Or is it a trick question?
I find no area at all!

$\text{I am asked to find the area inside of }r \:=\: 1+\cos4\theta\,\text{ and outside }\,r \,=\, 2.$

$r\,=\,2$ is a circle, center at the Origin (pole) with radius 2.

$r \:=\:1+\cos4\theta$ is a 4-leaf rose curve whose petals are 2 units long.

That is, it never ventures outside of the circle . . .

3. ## Re: Area between two polar equations

I made a typo indeed. It is r = 2+cos(4theta). So petals are 3 units long. Sorry again, my bad.

4. ## Re: Area between two polar equations

Originally Posted by richardsim10
to solve the region R bounded inside of r = 2+cos(4theta) and outside r = 2.

5. ## Re: Area between two polar equations

I finally managed to find my mistake. Angle is not pi/32, bur rather pi/8. I just made a stupid mental mistake.