Consider the parametric equations and for

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

Problem

Consider the parametric equations

x(t)=\sin t

and

y(t)=\cos 2t

for

0<t<2\pi

. Over which of the following intervals of

t

is the curve concave up with respect to

x

? (a)

0<t<\dfrac{\pi}{2}\text{ and }\dfrac{3\pi}{2}<t<2\pi

(b) The curve is never concave up on

0<t<2\pi

(c)

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

(d) All

t

0<t<2\pi

except

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