Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.4 Solve Trigonometric Equations - 14.4 Exercises - Skill Practice - Page 935: 12


$$x=\frac{5\pi }{4}+2\pi n,\:x=\frac{7\pi }{4}+2\pi nE$$

Work Step by Step

We solve the equation using the properties of trigonometric functions. Note, there is a general solution since trigonometric identities go up and down and this can pass through a given value of y many times. Solving this, we find: $$\sin \left(x\right)+\sqrt{2}=-\sin \left(x\right) \\ \sin \left(x\right)=-\frac{\sqrt{2}}{2} \\ x=\frac{5\pi }{4}+2\pi n,\:x=\frac{7\pi }{4}+2\pi n$$
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