For the curve with

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

Problem

For the curve

x = 2\cos t,\; y = 3\sin t

with

0\le t < 2\pi

, the tangent makes an angle of

45^{\circ}

with the positive

x

-axis at which one of the following parameter values? (a)

t = \tan^{-1}\!\left(\dfrac{3}{2}\right)

(b)

t = \pi - \tan^{-1}\!\left(\dfrac{3}{2}\right)

(c)

t = \pi - \tan^{-1}\!\left(\dfrac{2}{3}\right)

(d)

t = \dfrac{\pi}{2} + \tan^{-1}\!\left(\dfrac{3}{2}\right)