Answer:
Therefore the correct option is first one
[tex]\dfrac{\pi}{4}[/tex]
Step-by-step explanation:
Given:
[tex]\arcsin (\dfrac{\sqrt{2} }{2})[/tex]
To Find:
[tex]\arcsin (\dfrac{\sqrt{2} }{2})=?[/tex]
Solution:
The arcsin function is the inverse of the sine function.
It returns the angle whose sine is a given number.
So,
[tex]\sin \dfrac{\pi}{4}=\dfrac{1}{\sqrt{2}}[/tex]
Means: The sine of [tex]\dfrac{\pi}{4}[/tex] radian is [tex]\dfrac{1}{\sqrt{2}}[/tex]
∴ [tex]\arcsin (\dfrac{\sqrt{2}}{2})\\ Rationalizing \ we\ get\\\arcsin (\dfrac{\sqrt{2}}{2})=\arcsin (\dfrac{\sqrt{2}}{2}\times \dfrac{\sqrt{2}}{\sqrt{2} } )\\\\\arcsin (\dfrac{\sqrt{2}}{2})=\arcsin (\dfrac{1}{\sqrt{2}})[/tex]
Means: The angle whose sin is [tex]\dfrac{1}{\sqrt{2}}[/tex] is [tex]\dfrac{\pi}{4}[/tex] radian.
Therefore the correct option is first one
[tex]\dfrac{\pi}{4}[/tex]
