For in consider the region bounded between the curves (outer curve) and (inner curve)

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

Problem

For

\theta

[0,\pi]

consider the region

S(a)

bounded between the curves

r=a\sin\theta

(outer curve) and

r=2\sin\theta

(inner curve), where

a>2

. When

a=5

, the area of the region is

A

. For which of the following values of

a

will the area of the region be

1.5A

? (a)

a=6

(b)

a=4\sqrt{2}

(c)

a=\sqrt{35.5}

(d)

a=7