The polar curves and intersect at finitely many angles on the interval

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

Problem

The polar curves

r=3\cos\theta

and

r=3\sin\theta

intersect at finitely many angles on the interval

0\le\theta\le\pi

. Which of the following lists all such angles in that interval? (a)

\displaystyle \theta=\frac{\pi}{4},\,\frac{3\pi}{4}

(b)

\displaystyle \theta=\frac{\pi}{4},\,\frac{5\pi}{4}

(c)

\displaystyle \theta=\frac{\pi}{4}

(d)

\displaystyle \theta=\frac{\pi}{4},\,\frac{\pi}{2}