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: 116


$\{\frac{\pi}{4}, 2.5536, \frac{5\pi}{4}, 5.6952 \}$

Work Step by Step

Step 1. Factor the equation as $(3tan(x)+2)(tan(x)-1)=0$, thus $tan(x)=1$ and $tan(x)=-\frac{2}{3}$ Step 2. For $tan(x)=1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{4},\frac{5\pi}{4}$ Step 3. For $tan(x)=-\frac{2}{3}$, we can find the reference angle as $x_0=tan^{-1}(\frac{2}{3})\approx0.5880$ and all x-values in $[0,2\pi)$ as $x=\pi-x_0\approx2.5536$ and $x=2\pi-x_0\approx5.6952$ Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{\pi}{4}, 2.5536, \frac{5\pi}{4}, 5.6952 \}$
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