## Precalculus (6th Edition)

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