A point moves in the plane with polar coordinates given by and

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

Problem

A point moves in the plane with polar coordinates given by

r=2t

and

\theta=t^{2}

, where

t

is measured in seconds. Let

x=r\cos\theta

denote the

x

-coordinate of the point. What is

\dfrac{dx}{dt}

t=1

? (a)

2\sin 1-4\cos 1

(b)

2\cos 1+4\sin 1

(c)

2\cos 1-4\sin 1

(d)

2\cos 1-2\sin 1