Answer
$-45^{o}$
Work Step by Step
Solve for radians, then convert to degrees.
$y=\tan^{-1} x$
Domain: $(-\infty, \infty) $
Range: $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$
-------------
$y$ is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ such that $\tan y=-1$
$\displaystyle \tan(-\frac{\pi}{4})=-1\qquad$and$\displaystyle \quad -\frac{\pi}{4}\in(-\frac{\pi}{2}, \displaystyle \frac{\pi}{2})$,
so
$y =-\displaystyle \frac{\pi}{4}$
To convert radians to degrees, multiply y with $\displaystyle \frac{180^{o}}{\pi}$
$\displaystyle \theta=-\frac{\pi}{4}\cdot\frac{180^{o}}{\pi}=-45^{o}$
