Answer
$-\dfrac {\sqrt 2 }{2}$
Work Step by Step
$\sin \left( 315 ^0\right) =\sin \left( 360^0-45^0\right) =\sin \left( 2\pi -\dfrac {\pi }{4}\right) =\sin 2\pi \cos \dfrac {\pi }{4}-\cos 2\pi \sin \dfrac {\pi }{4}=0-\sin \dfrac {\pi }{4}=-\dfrac {\sqrt 2 }{2}$
