Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.7 Equations Involving Inverse Trigonometric Functions - 7.7 Exercises - Page 728: 9


$x=\displaystyle \frac{1}{2}\arctan\frac{y}{3}$

Work Step by Step

The goal is to isolate x. Divide with 3... $\displaystyle \frac{y}{3}=\tan 2x\qquad$ ...use the definition of arctan $2x=\displaystyle \arctan\frac{y}{3}$ (2x is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ such that $\displaystyle \tan\frac{y}{3}=2x$) (...If $2x\displaystyle \in(-\frac{\pi}{2}, \displaystyle \frac{\pi}{2})$, then $x\displaystyle \in(-\frac{\pi}{4}, \displaystyle \frac{\pi}{4})$...) ... divide with 2 ... $x=\displaystyle \frac{1}{2}\arctan\frac{y}{3}$
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