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: 55


$\{\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6} \}$

Work Step by Step

Step 1. The equation gives two solutions $cos(x)=-\frac{\sqrt 3}{2}$ and $sin(x)=-\frac{1}{2}$ Step 2. For $cos(x)=-\frac{\sqrt 3}{2}$, we can find all x-values in $[0,2\pi)$ as $x=\frac{5\pi}{6}, \frac{7\pi}{6}$ Step 3. For $sin(x)=-\frac{1}{2}$, we can find all x-values in $[0,2\pi)$ as $x=\frac{7\pi}{6},\frac{11\pi}{6}$ Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6} \}$
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