Answer
arctan($-1$)$=-45^{o}$
Work Step by Step
Inverse Tangent Function
$y=\tan^{-1}x$ or $y=$ arctan $x$ means that $x=\tan y$, for $-\displaystyle \frac{\pi}{2} < y < \frac{\pi}{2}$.
Or for an angle in degrees,
$\theta=\tan^{-1}x$ means $ x=\tan\theta$,
for $-90^{o} < \theta < 90^{o}$.
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Knowing: $\quad \tan 45^{o}=1$,
(and $\tan(-\theta)=-\tan\theta),$
we find $\theta=-45^{o}$ from the interval $-90^{o} < \theta < 90^{o}$
such that
$\tan$($-45^{o})=-1.$
So,
arctan($-1$)$=-45^{o}$
