A point on the curve has Cartesian coordinates

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

Problem

A point on the curve

r=3\bigl(1+\cos\theta\bigr)

has Cartesian coordinates

(x,y)

, where

x=r\cos\theta

and

y=r\sin\theta

. For

0\le\theta\le\pi

, which value of

\theta

maximizes the

y

-coordinate of the point? (a)

\dfrac{\pi}{2}

(b)

\dfrac{\pi}{4}

(c)

\dfrac{\pi}{3}

(d)

\dfrac{2\pi}{3}