Which expression equals for a particle whose position in Cartesian coordinates is…

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

Problem

Which expression equals

\dfrac{dx}{dt}

for a particle whose position in Cartesian coordinates is given by

x=r\cos\theta

and

y=r\sin\theta

, where

r=r(\theta)

and

\theta=\theta(t)

? (a)

-r\sin\theta\,\dfrac{d\theta}{dt}

(b)

\left(\dfrac{dr}{d\theta}\cos\theta - r\sin\theta\right)

(c)

\left(\dfrac{dr}{d\theta}\cos\theta - r\sin\theta\right)\dfrac{d\theta}{dt}

(d)

\left(\dfrac{dr}{d\theta}\cos\theta + r\sin\theta\right)\dfrac{d\theta}{dt}