Answer
(a) $F(x)=\frac{1}{2}cos(x)-\frac{1}{2}cos(2x)$
(b) See graph (red).
Work Step by Step
(a) $F(x)=sin(3x)sin(x)=\frac{1}{2}cos(\frac{3x-x}{2})-\frac{1}{2}cos(\frac{3x+x}{2})=\frac{1}{2}cos(x)-\frac{1}{2}cos(2x)$
(b) See graph (red).
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 7 - Applications of Trigonometric Functions - Section 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves - 7.5 Assess Your Understanding - Page 575: 34
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