Answer
$\dfrac {\sqrt 2}{2}$
Work Step by Step
$\sin \left( 405^0\right) =\sin \left( 360^0+45^0\right) =\sin \left( 2\pi +\dfrac {\pi }{4}\right) =\sin 2\pi \cos \dfrac {\pi }{4}+\cos 2\pi \sin \dfrac {\pi }{4}=0+1\times \sin \dfrac {\pi }{4}=\sin \dfrac {\pi }{4}=\dfrac {\sqrt 2}{2}$
