A cycloid is traced by and for

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

Problem

A cycloid is traced by

x(t)=t-\sin t

and

y(t)=1-\cos t

for

t\ge 0

. What is the smallest positive value of

t

at which the curve has a horizontal tangent? (a)

2\pi

(b)

\pi

(c)

0

(d)

\dfrac{\pi}{2}