Let be the area enclosed by on

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

Problem

Let

A_1

be the area enclosed by

r=a\sin\theta

0\le\theta\le\pi

, and let

A_2

be the area enclosed by

r=a\sin 2\theta

0\le\theta\le\tfrac{\pi}{2}

, where

a>0

. What is the value of the ratio

\dfrac{A_1}{A_2}

? (a)

1

(b)

2

(c)

\dfrac{1}{2}

(d) 4