I had the following problem:
Obtain the area of the region of the circle with $r = 1$ that is exterior from the area of a cycloid given by $r(\theta) = 1 - \cos\theta $
My idea was just to subtract the functions and put them in the area formula. Here's what I did:
$$A = \int \big[(1-\cos\theta)-(1)\big]^2 d\theta = \int (-\cos\theta)^2 d\theta = \frac{1}{2}\theta + \frac{1}{4}\sin(2\theta)$$
I don't know if my procedure was right. I think the problem statement was vague so I got confused to what it was asking.
Have a look at the graph first.
I do not find the problem statement vague. It is asking to calculate the area of white portion in the circle of radius $1.$
Also, you have to put the limits for $\theta$ and solve. Try again and if you still have problem, have a look at http://tutorial.math.lamar.edu/Classes/CalcII/PolarArea.aspx (There are more problems in this link which are similar to this one).