Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.3 Trigonometric Equations - 7.3 Assess Your Understanding - Page 466: 38


General formula for solutions: $\dfrac{\pi}{4}+k\pi$, where $k$ is an integer Six solutions: $\left\{\dfrac{\pi}{4}, \dfrac{5\pi}{4}\pi, \dfrac{9\pi}{4}, \dfrac{13\pi}{4}, \dfrac{17\pi}{4}, \dfrac{21\pi}{4}\right\}$

Work Step by Step

$\tan\theta=1$ Since the period of tangent is $\pi$, then the solutions are: $\theta=\frac{1}{4}\pi+k\pi$ where $k$ is an integer Six possible solutions are: $k=0$ $\theta=\frac{1}{4}\pi+(0)\pi=\frac{1}{4}\pi$ $k=1$ $\theta=\frac{1}{4}\pi+(1)\pi=\frac{5}{4}\pi$ $k=2$ $\theta=\frac{1}{4}\pi+(2)\pi=\frac{9}{4}\pi$ $k=3$ $\theta=\frac{1}{4}\pi+3\pi=\frac{13}{4}\pi$ $k=4$ $\theta=\frac{1}{4}\pi+4\pi=\frac{17}{4}\pi$ $k=5$ $\theta=\frac{1}{4}\pi+(5)\pi=\frac{21}{4}\pi$
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