Answer
$-\dfrac {\sqrt {2}}{4}\left( 1+\sqrt {3}\right) $
Work Step by Step
$\sin \left( -\dfrac {7\pi }{12}\right) =-\sin \left( \dfrac {7\pi }{12}\right) =-\sin \left( \dfrac {\pi }{3}+\dfrac {\pi }{4}\right) =-\left( \sin \dfrac {\pi }{3}\cos \dfrac {\pi }{4}+\cos \dfrac {\pi }{3}\sin \dfrac {\pi }{4}\right) =-\left( \dfrac {\sqrt {3}}{2}\times \dfrac {\sqrt {2}}{2}+\dfrac {1}{2}\times \dfrac {\sqrt {2}}{2}\right) =-\dfrac {\sqrt {2}}{4}\left( 1+\sqrt {3}\right) $
