Chapter 13, Problem 4RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find parametric equations for the tangent line to the curve *x* = 2 sin *t*, *y* = 2 sin 2*t*, *z* = 2 sin 3*t* at the point (l,

To determine

**To find:** The parametric equations for the tangent line to the curve with the parametric equations

Explanation

**Formula used:**

Write the expression to find the parametric equations for a line through the point

Write the required differentiation formulae to find the tangent vector

Write the parametric equations of the curve as follows:

Write the vector equation from the parametric equations of the curve as follows:

The tangent vector of the curve is the derivative of the vector function

**Calculation of the derivative of the vector function**
**:**

To find the derivative of the vector function, differentiate each component of the vector function.

Differentiate each component of the vector function

Rewrite and compute the expression as follows:

As the scalar parameter

**Calculation of the point on the required line:**

Substitute

The point on the required line is

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