The rose curve consists of three congruent petals

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

Problem

The rose curve

r = 2\sin(3\theta)

consists of three congruent petals. What is the exact area of a single petal? (a)

\dfrac{2\pi}{9}

(b)

\dfrac{\pi}{3}

(c)

\dfrac{\pi}{6}

(d)

\dfrac{2\pi}{3}