Answer
$-\dfrac{\sqrt2}{2}$
Work Step by Step
We know that $\sin$, $\csc$, $\tan$ are odd functions, which means $f(-\theta)=-f(\theta).$
We also know that $\cos$, $\sec$, are even functions, which means $f(-\theta)=f(\theta).$
Therefore,
$\sin(-135^{o})=-\sin(135^{o})=-\dfrac{\sqrt2}{2}$
