For , a curve is given by and . Which of the following lists all values of in the…

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

Problem

For

t\in[0,2\pi]

, a curve is given by

x=\sin(2t)

and

y=t-\cos t

. Which of the following lists all values of

t

in the stated interval at which the curve has a vertical tangent line? (a)

\dfrac{\pi}{2},\;\dfrac{3\pi}{2}

(b)

\dfrac{\pi}{4},\;\dfrac{3\pi}{4},\;\dfrac{5\pi}{4},\;\dfrac{7\pi}{4}

(c)

\dfrac{\pi}{4},\;\dfrac{5\pi}{4}

(d)

\dfrac{3\pi}{4},\;\dfrac{7\pi}{4}