Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.2 The Unit Circle and Circular Functions - 6.2 Exercises - Page 589: 78

Answer

$\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3}$

Work Step by Step

1. Given $tan^2(s)=3$, we have $tan(s)=\pm\sqrt 3$. 2. For $tan(s)=\sqrt 3$, we can find a reference angle as $s_0=tan^{-1}(\sqrt 3)=\frac{\pi}{3}$. In $[0,2\pi)$, there are two solution angles $s=\frac{\pi}{3}, \pi+\frac{\pi}{3}$ or $s=\frac{\pi}{3}, \frac{4\pi}{3}$ 3. For $tan(s)=-\sqrt 3$, we can find a reference angle as $s_0=tan^{-1}(\sqrt 3)=\frac{\pi}{3}$. In $[0,2\pi)$, there are two solution angles $s=\pi-\frac{\pi}{3}, 2\pi-\frac{\pi}{3}$ or $s=\frac{2\pi}{3}, \frac{5\pi}{3}$ 4. The solutions are $\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3}$
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