Find the unit tangent vector T(t) at the given value

Question

For the parameterized curve find the unit tangent vector T(t) at the given value of t

r(t) =<3 sin(2t), 13, cos(4t)>, for 0 <= t<= pi, t=pi/2

T(pi/2)=?

Answer 1

Vector V tangent to curve r(t): V(u) = r(π/2) + ur'(π/2) = <3sin(π), 13, cos(2π)> + u<6cos(π), 0, - 4sin(2π)> =

<0, 13, 1> + u<-6, 0, 0> = < - 6u,13,1>.

Unit vector v =,<-6u, 13,1>/√(36u² + 170)