Find the unit tangent vector at the given point on the curve.

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

Problem

Find the unit tangent vector

\mathbf{T}(t)

at the given point on the curve.

\mathbf{r}(t) = \sin t \mathbf{i} + 5t \mathbf{j} + \cos t \mathbf{k}, (0, 0, 1)