For a polar curve given by

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

Problem

r=f(\theta)

, which of the following expressions equals the slope

\dfrac{dy}{dx}

in terms of

\theta

? (a)

\dfrac{\dfrac{dr}{d\theta}\cos\theta-r\sin\theta}{\dfrac{dr}{d\theta}\sin\theta+r\cos\theta}

(b)

\dfrac{\dfrac{dr}{d\theta}\sin\theta+r\cos\theta}{\dfrac{\,dr}{d\theta}\cos\theta+r\sin\theta}

(c)

\dfrac{\dfrac{dr}{d\theta}\sin\theta+r\cos\theta}{\dfrac{dr}{d\theta}\cos\theta-r\sin\theta}

(d)

\dfrac{\dfrac{dr}{d\theta}\cos\theta+r\sin\theta}{\dfrac{dr}{d\theta}\sin\theta-r\cos\theta}