What is \sin ( sin^{-1} frac{sqrt{2}}{2})?

Arcsine is also known as $\arcsin$ and ${\sin}^{-} 1$
Sine is also known as $\sin$
$\sin \left({\sin}^{-} 1 \frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}$