For the unit circle parametrized by

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

Problem

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

, let

t_{1}=\dfrac{\pi}{4}

. Determine the other value

t_{2}

in the interval

[0,2\pi)

such that the tangent line at

t_{2}

is parallel to the tangent line at

t_{1}