(a) Find the point of intersection of the tangent lines to the curve at the points…

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

Problem

(a) Find the point of intersection of the tangent lines to the curve

\mathbf{r}(t) = \langle \sin \pi t, 2 \sin \pi t, \cos \pi t \rangle

at the points where

t = 0

and

t = 0.5

. (b) Illustrate by graphing the curve and both tangent lines.