A cycloid is traced by the parametric equations 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 the parametric equations

x(t)=t-\sin t

and

y(t)=1-\cos t

for

0\le t\le 2\pi

. What is the value of

\dfrac{d^{2}y}{dx^{2}}

at

t=\pi

? (a)

0

(b)

\dfrac{1}{4}

(c)

-\dfrac{1}{4}

(d)

-\dfrac{1}{8}

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