# How do you do simplify sin^-1(sqrt2/2)?

Apr 11, 2016

${\sin}^{- 1} \left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4}$

#### Explanation:

${\sin}^{- 1} a$ means an angle whose sine is $a$.

Now $\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{1}{\sqrt{2}}$

and we know $\sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$

Hence

${\sin}^{- 1} \left(\frac{\sqrt{2}}{2}\right) = {\sin}^{- 1} \left(\frac{1}{\sqrt{2}}\right) = \frac{\pi}{4}$