Consider the curve given by and for

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

Problem

Consider the curve given by

x(t)=e^{t}\cos t

and

y(t)=e^{t}\sin t

for

-2\pi\le t\le 2\pi

. Determine all values of

t

in this interval at which the tangent line to the curve is vertical.