curve R(t) Find the parametric equations of the tangent line to the (2t, cos 2t, sin 2t) at the point (0, 1, 0). I =

What is Tangent Line:

The straight line that only touches the curve at a particular location is referred to as the tangent line or simply the tangent to a plane curve in geometry. The tangent line is "moving in the same direction" as the curve when it passes through the place where the curve and the tangent line meet, known as the point of tangency, and is thus the best straight-line approximation to the curve at that location. The graph of the affine function that most closely resembles the original function at the specified location is known as the tangent line to a point on a differentiable curve, also known as a tangent line approximation.

Given:

Given curve is .

To Determine:

We determine the equation of tangent line to the given curve at $\left(0,1,0\right)$.