Chapter 13.2, Problem 7E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Sketch the plane curve with the given vector equation.

(b) Find **r***'*(*t*).

(c) Sketch the position vector **r**(*t*) and the tangent vector **r***'*(*t*) for the given value of *t*.

**7.** **r**(*t*) = 4 sin *t* **i** − 2 cos *t* **j**, *t* = 3π/4

**(a)**

To determine

**To sketch:** The plane curve with the vector equation

Explanation

Write the *x*-component of the vector

Rearrange the expression as follows.

Take square on both sides.

Write the *y*-component of the vector

Rearrange the expression

Take square on both sides of the expression.

Add equation (1) with equation (2) as follows.

The curve

The required curve is a graph of

Find the vector

**(b)**

To determine

**To find:** The vector

**(c)**

To determine

**To sketch:** The position vector

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