Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 118

Answer

$(\frac{7\pi}{6}, -\frac{3}{2})$ and $(\frac{11\pi}{6}, -\frac{3}{2})$; see graph.
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Work Step by Step

Step 1. Graph $f(x)$ (red curve) and $g(x)$ (blue curve) as shown in the figure. Step 2. Let $f(x)=g(x)$; we have $3sin(x)=sin(x)-1$ or $sin(x)=-\frac{1}{2}$, which gives solutions in $[0,2\pi]$ as $x=\frac{7\pi}{6}$ and $x=\frac{11\pi}{6}$ corresponding to points of intersection $(\frac{7\pi}{6}, -\frac{3}{2})$ and $(\frac{11\pi}{6}, -\frac{3}{2})$ Step 3. We can identify the above points as shown on the graph.
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