Precalculus (6th Edition) Blitzer

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

Chapter 4 - Section 4.6 - Graphs of Other Trigonometric Functions - Exercise Set - Page 610: 56

Answer

$\{ -\frac{5\pi}{4}, -\frac{\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4} \}$
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Work Step by Step

Step 1. Rewrite the equation as $cot(x)+1=0$ and define a function $f(x)=cot(x)+1$. Step 2. Graph the function in the interval of $[-2\pi,2\pi]$ as shown in the figure. Step 3. Identify zeros as $x=-\frac{5\pi}{4}, -\frac{\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4}$ Step 4. We conclude the solution set in $[-2\pi,2\pi]$ is $\{ -\frac{5\pi}{4}, -\frac{\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4} \}$
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