Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.3 - Solving Trigonometric Equations - 7.3 Exercises - Page 531: 49


$x\approx3.553$ and $x\approx5.872$

Work Step by Step

One of the solutions can be found by using the inverse function: $5~sin~x+2=0$ $5~sin~x=-2$ $sin~x=\frac{-2}{5}$ $x=arcsin(-0.4)=-0.412~rad~~$ (it lies in the range $[-\frac{\pi}{2},\frac{\pi}{2}]$) $x=-0.412~rad+2\pi=5.872~rad~~$ (now it lies in the interval $[0,2\pi)$)
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