For the parametric curve with

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

Problem

For the parametric curve

x = t - \sin t,\; y = 1 - \cos t

with

0 < t < 2\pi

, the slope of the tangent equals

\dfrac{1}{2}

at which of the following values of

t

? (a)

t = \pi - 2\tan^{-1}2

(b)

t = \tan^{-1} 2

(c)

t = 2\tan^{-1} 2

(d)

t = 2\tan^{-1}\!\bigl(\tfrac{1}{2}\bigr)