# Find the area of the region that lies inside both curves. r = 5 sin(θ), r = 5 cos(θ) [closed]

I am completely blanking on this question and I really don't even know where to start.

## closed as off-topic by Leucippus, Shailesh, JMP, user91500, zhorasterDec 15 '16 at 6:12

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Solving for the point of intersection of the two curves, we get $$5\sin \theta =5\cos \theta$$ $$\Rightarrow \tan \theta =1$$ $$\Rightarrow \theta =\frac {\pi}{4} \mid \frac {5\pi}{4}$$ where $\mid$ stands for "or".
To calculate the area, we use the formula $$\frac {1}{2}\int_{a}^{b}(r_1^2-r_2^2) d\theta$$ where $a$ and $b$ are the coordinates of intersection.
Now using $r_1 = 5\sin \theta$ and $r_2 = 5\cos \theta$ and $a =\frac {\pi}{4}$ and $B =\frac {5\pi}{4}$, you shall be able to easily calculate your integral.