MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Two polar curves are given by r=3cosθ and r=3sinθ. Consider the region that is simultaneously inside both curves and lies in the first quadrant.
(a) Determine all values of θ in [0,2π] at which the two curves intersect.
(b) For each subinterval of [0,2π] determined in part (a), state which curve provides the outer boundary of the region that is inside both curves. Justify your answer.
(c) Write, but do not evaluate, a definite integral or sum of definite integrals that represents the exact area of the described region.