## Trigonometry (11th Edition) Clone

arctan($-1$)$=-45^{o}$
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 $-90^{o} < \theta < 90^{o}$. --------------- 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($-1$)$=-45^{o}$