The curves and intersect at

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

Problem

The curves

r=2\sin\theta

and

r=2\cos\theta

intersect at

\theta=\tfrac{\pi}{4}

. Determine the exact area, in square units, of the region in the first quadrant that lies inside

r=2\sin\theta

and outside

r=2\cos\theta