Let for . Which of the following gives as a function of…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let

r=3\theta

for

0\le \theta\le 2

. Which of the following gives

\dfrac{dy}{dx}

as a function of

\theta

? (a)

\displaystyle \tan\theta

(b)

\displaystyle \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}

(c)

\displaystyle \frac{\cos\theta+\theta\sin\theta}{\sin\theta-\theta\cos\theta}

(d)

\displaystyle \frac{\sin\theta-\theta\cos\theta}{\cos\theta+\theta\sin\theta}