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: 115


$\{\frac{3\pi}{4}, 2.1588, \frac{7\pi}{4}, 5.3004 \}$

Work Step by Step

Step 1. Factor the equation as $(2tan(x)+3)(tan(x)+1)=0$; thus $tan(x)=-1$ and $tan(x)=-1.5$ Step 2. For $tan(x)=-1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{3\pi}{4},\frac{7\pi}{4}$ Step 3. For $tan(x)=-1.5$, we can find the reference angle as $x_0=tan^{-1}(1.5)\approx0.9828$ and all x-values in $[0,2\pi)$ as $x=\pi-x_0\approx2.1588$ and $x=2\pi-x_0\approx5.3004$ Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{3\pi}{4}, 2.1588, \frac{7\pi}{4}, 5.3004 \}$
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