Answer
$-\displaystyle \frac{\pi}{4}$
Work Step by Step
lnverse Tangent Function:
$y=\tan^{-1}x$ or $y=$ arctan $x \quad $means that
$x=\tan y$, for $-\displaystyle \frac{\pi}{2} < y < \frac{\pi}{2}$.
----------
In the interval$\quad -\displaystyle \frac{\pi}{2} < y < \frac{\pi}{2}$ ,
we find $y=-\displaystyle \frac{\pi}{4}$ to be such that $\displaystyle \tan(-\frac{\pi}{4})=-1$.
So
$y=\displaystyle \tan^{-1}(-1)=-\frac{\pi}{4}$
