Question

What is the value of Arc sine (StartFraction StartRoot 2 EndRoot Over 2 EndFraction)? StartFraction pi Over 6 EndFraction StartFraction pi Over 4 EndFraction StartFraction 7 pi Over 4 EndFraction StartFraction 11 pi Over 6 EndFraction

Answer 1

Given:

The expression is

$arcsine\left(\dfrac{\sqrt{2}}{2}\right)$

To find:

The value of given expression.

Solution:

We have,

$arcsine\left(\dfrac{\sqrt{2}}{2}\right)$

It can be rewritten as

$=\sin^{-1}\left(\dfrac{\sqrt{2}}{2}\right)$

$=\sin^{-1}\left(\dfrac{1}{\sqrt{2}}\right)$

$=\sin^{-1}\left(\sin \dfrac{\pi}{4}}\right)$

$=\dfrac{\pi}{4}$

Therefore, the correct option is B.