Precalculus (6th Edition) Blitzer

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

Chapter 5 - Review Exercises - Page 709: 56

Answer

$\frac{3\pi}{2}$

Work Step by Step

Step 1. Given the equation $tan(\frac{x}{2})=-1$, we can find the solution in $[0,\pi)$ as $\frac{x}{2}=\frac{3\pi}{4}$ or $x=\frac{3\pi}{2}$ Step 2. Consider the original function has a period of $2\pi$; we can express all the solutions as $x=2k\pi+\frac{3\pi}{2}$ where $k$ is an integer. Thus, within $[0,2\pi)$, we have $x= \frac{3\pi}{2}$ as the solution to the original equation.
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