# How do you find the value for tan ^ -1 ( -1)?

$- \frac{\pi}{4}$
We know that $\tan \left(- x\right) = - \tan \left(x\right) \forall x \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$, and that $\tan \left(\frac{\pi}{4}\right) = 1$.
Therefore, $\tan \left(- \frac{\pi}{4}\right) = - 1$, which in turn implies ${\tan}^{- 1} \left(- 1\right) = - \frac{\pi}{4}$.