Consider the polar curves and for

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider the polar curves

r=2+2\sin\theta

and

r=3

for

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

. Which statement best describes which curve forms the outer boundary of the region bounded by the two curves on this interval? (a)

r=3

is the outer curve for every

\theta

\, in the interval. (b)

r=2+2\sin\theta

is the outer curve for

0\le\theta<\frac{\pi}{6}

, and

r=3

is the outer curve for

\frac{\pi}{6}<\theta\le\frac{\pi}{2}

. (c)

r=3

is the outer curve for

0\le\theta<\frac{\pi}{6}

, and

r=2+2\sin\theta

is the outer curve for

\frac{\pi}{6}<\theta\le\frac{\pi}{2}

. (d)

r=3

is the outer curve for

0\le\theta<\frac{\pi}{3}

, and

r=2+2\sin\theta

is the outer curve for

\frac{\pi}{3}<\theta\le\frac{\pi}{2}