For , consider the curves and . On which sub-interval of does lie outside…

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

Problem

For

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

, consider the curves

r=2

and

r=3\sin\theta

. On which sub-interval of

[0,\tfrac{\pi}{2}]

does

r=3\sin\theta

lie outside

r=2

? (a) on the entire interval

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

(b) for

\dfrac23\le\theta\le\tfrac{\pi}{2}

\arcsin\!\left(\tfrac23\right)\le\theta\le\tfrac{\pi}{2}

(d) for

0\le\theta\le\arcsin\!\left(\tfrac23\right)