How do you find the exact value of $sin ({cos}^{- 1} (\frac{\sqrt{2}}{2}))$ $sin(cos^-1 (sqrt2/2))$ ?

Question

1998 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-13T03:20:06

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

The angle $a = {cos}^{- 1} (\frac{\sqrt{2}}{2}) \in Q 1$ $a = cos^(-1)(sqrt 2/2) in Q1$ .

Use $sin a = \pm \sqrt{1 - {cos}^{2} a}$ $sin a = +-sqrt(1-cos^2a)$ and the positive sign is for $a \in Q 1$ $a in Q1$ .

Here, the given expression is

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

How do you find the exact value of sin(cos−1(√22))sin(cos^-1 (sqrt2/2))?