# How do you find the exact value of sin(cos^-1 (sqrt2/2))?

Aug 13, 2016

$\frac{1}{\sqrt{2}}$

#### Explanation:

The angle $a = {\cos}^{- 1} \left(\frac{\sqrt{2}}{2}\right) \in Q 1$.

Use $\sin a = \pm \sqrt{1 - {\cos}^{2} a}$ and the positive sign is for $a \in Q 1$.

Here, the given expression is

$\sin a = \frac{1}{\sqrt{2}}$.