Calculus parametric

Question

Find the parametric equations for x,y,z the line that is tangent to the given curve at the given parameter value

t=t0. r(t)=(sint)i+(cost)j+(sin6t)k​, t0= 3pi/2

Answer 1

r'(t) = (cost)i + (-sint)j + (6cos6t)k[

r(3π/2) = - i; r'(3π/2) = j - 6k;

So, parametric equation of tangent line: x = -1, y = t, z = - 6t