Consider the curve for

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

Problem

Consider the curve

x=\sin t,\;y=t+\cos t

for

0\le t<2\pi

. At which value(s) of

t

does the curve have a vertical tangent? (a)

t=\dfrac{\pi}{2}

only (b)

t=\dfrac{\pi}{2}

and

t=\dfrac{3\pi}{2}

(c)

t=\dfrac{3\pi}{2}

only (d) The curve has no vertical tangent in the given interval