Chapter 12.2, Problem 42E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

(a) Find the unit vectors that are parallel to the tangent line to the curve *y* = 2 sin *x* at the point (π/6, 1).

(b) Find the unit vectors that are perpendicular to the tangent line.

(c) Sketch the curve *y* = 2 sin *x* and the vectors in parts (a) and (b), all starting at (π/6, 1).

(a)

To determine

**To find**: The parallel unit vectors to the tangent line of

Explanation

**Given:**

Equation of curve is

**Formula used:**

Write the expression for slope of function

Here,

Write the expression for magnitude of vector

Write the expression for unit vectors of vector **a**

Find the slope of equation

Substitute
*y*,

Substitute
*x*

(b)

To determine

**To find**: The perpendicular unit vectors to the tangent line of

(c)

To determine

**To sketch**: curve of

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