Answer
$-\dfrac{\sqrt{2}}{2}$
Work Step by Step
The sine is an odd function so
$\sin{(-\theta)} = - \sin{\theta}$
Thus,
$\sin{(-135 ^{\circ})} = -\sin{(135^{\circ})}$
Due to symmetry of the unit circle $\sin{(135^{\circ})} = \sin{(45^{\circ})}$
Hence,
$\sin{(-135 ^{\circ})} = -\sin{(45^{\circ})} =\boxed{-\dfrac{\sqrt{2}}{2}}$
