Answer
$-\frac{\sqrt2}{2}$
Work Step by Step
First, we solve tan$^{-1}(-1)$. The interval of the inverse of tangent is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a slope of $-1$ in that interval. The answer is $-\frac{\pi}{4}$
Now, we can solve sin$\left(-\frac{\pi}{4}\right)$ which is $-\frac{\sqrt2}{2}$