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: 27


$$x=\frac{\pi }{3}+\pi n,\:x=\frac{2\pi }{3}+\pi n$$

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: $$\text{Considering only the real solutions:} \\ \tan \left(x\right)=\sqrt{3},\:\tan \left(x\right)=-\sqrt{3} \\ x=\frac{\pi }{3}+\pi n,\:x=\frac{2\pi }{3}+\pi n$$
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