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I'm having trouble with the following question:

Find the area of the region inside both of the circles $r = 2a\cos(\theta)$ and $r = 2a\sin(\theta)$, where a is a positive constant.

From what I think i have correct the region is:

$2a\sin(\theta) \le r \le 2a\cos(\theta)$

$0 \le \theta \le \frac{\pi}{4}$

My real question is would it be advantegous to convert this back to cartesian coordinates, or even possible to do that?

I think if I integrate everything according to those functions, I end up with something like

$$\int_0^\frac{\pi}{4} \big(\cos(\theta)^2 - \sin(\theta)^2\big) d\theta$$

Not exactly the nicest function

Thanks for the help guys! Sorry if I have made any formatting errors, I'm new to the math stackexchange.

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1 Answer

up vote 0 down vote accepted

$$\cos^2\theta-\sin^2\theta=\cos2\theta\;.$$

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