Consider the polar graph given by for .

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

Problem

Consider the polar graph given by

r=3+2\sin\theta

for

0\le\theta\le 2\pi

. (1) Determine the exact area that is enclosed by the entire curve. (2) State whether the curve is traced exactly once on the interval

0\le\theta\le 2\pi

. Justify your answer using properties of

r

on this interval.