Answer
$-\dfrac{\sqrt2}{2}.$
Work Step by Step
Note that $\tan^{-1}{\left(-1\right)}=-\dfrac{\pi}{4}$, because $\tan{\left(-\dfrac{\pi}{4}\right)}=-1$ and $-\dfrac{\pi}{4}$ is in the range of $\tan^{-1}{x}$, which is $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right].$
Thus
$\sin{\left(\tan^{-1}{\left(-1\right)}\right)}=\sin{\left(-\dfrac{\pi}{4}\right)}=-\dfrac{\sqrt2}{2}.$
