# Thread: Area between two polar curves

1. ## Area between two polar curves

I am having difficulty finding the area between these two curves:

$\displaystyle r = \sin{2\Theta}$ and $\displaystyle r = \cos{2\Theta}$

I setup the integral like this:

$\displaystyle \int_{0}^{\pi^/8}1/2(\cos{2\Theta}^2 - \sin{2\Theta}^2) d\Theta$

I multiply the answer of the integral by 16 for the 16 parts of the graph but I cannot arrive at the right answer.
Any help is appreciated of where I am going wrong.

Thanks

2. Originally Posted by evant8950
I am having difficulty finding the area between these two curves:

$\displaystyle r = \sin{2\Theta}$ and $\displaystyle r = \cos{2\Theta}$

I setup the integral like this:

$\displaystyle \int_{0}^{\pi^/8}1/2(\cos{2\Theta}^2 - \sin{2\Theta}^2) d\Theta$

I multiply the answer of the integral by 16 for the 16 parts of the graph but I cannot arrive at the right answer.
Any help is appreciated of where I am going wrong.

Thanks
Draw the graphs of each. Although they intersect at the origin, the point with polar coordinates [0, 0] is NOT common to both curves ....

3. Originally Posted by mr fantastic
Draw the graphs of each. Although they intersect at the origin, the point with polar coordinates [0, 0] is NOT common to both curves ....
When I set them equal I get they intersect at $\displaystyle \pi/8$. How do I find the other point of intersection?

Thanks