Find t in a Parametric Equation

[Jimerd]

Homework Statement

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 6 cos t, y = 6 sin t, z = 6 cos 2t; (3√3, 3, 3)

Homework Equations

The Attempt at a Solution

So I understand that r(t)= 6cost t, 6sint, 6cos2t

and r'(t)= -6sint, 6cost, -12sin2t

So here is the questions, how do I find what the value of t is at points (3√3, 3, 3)

 

[SammyS]

Homework Statement

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 6 cos t, y = 6 sin t, z = 6 cos 2t; (3√3, 3, 3)

Homework Equations

The Attempt at a Solution

So I understand that r(t)= 6cost t, 6sint, 6cos2t

and r'(t)= -6sint, 6cost, -12sin2t

So here is the questions, how do I find what the value of t is at points (3√3, 3, 3)

Solve (6cost t, 6sint, 6cos2t) = (3√3, 3, 3) for t .