The circle and the curve intersect at and

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The circle

r=2

and the curve

r=4\sin\theta

intersect at

\theta=\tfrac{\pi}{6}

and

\theta=\tfrac{5\pi}{6}

. Calculate the exact area of the region that lies inside

r=4\sin\theta

and outside

r=2

between these angles.