Question

What is the value of arcsin(2√2)? answer: it's the picture attached. ​

Answer 1

Answer:

Therefore the correct option is first one

$\dfrac{\pi}{4}$

Step-by-step explanation:

Given:

$\arcsin (\dfrac{\sqrt{2} }{2})$

To Find:

$\arcsin (\dfrac{\sqrt{2} }{2})=?$

Solution:

The arcsin function is the inverse of the sine function.

It returns the angle whose sine is a given number.

So,

$\sin \dfrac{\pi}{4}=\dfrac{1}{\sqrt{2}}$

Means: The sine of $\dfrac{\pi}{4}$ radian is $\dfrac{1}{\sqrt{2}}$

∴ $\arcsin (\dfrac{\sqrt{2}}{2})\\ Rationalizing \ we\ get\\\arcsin (\dfrac{\sqrt{2}}{2})=\arcsin (\dfrac{\sqrt{2}}{2}\times \dfrac{\sqrt{2}}{\sqrt{2} } )\\\\\arcsin (\dfrac{\sqrt{2}}{2})=\arcsin (\dfrac{1}{\sqrt{2}})$

Means: The angle whose sin is $\dfrac{1}{\sqrt{2}}$ is $\dfrac{\pi}{4}$ radian.

Therefore the correct option is first one

$\dfrac{\pi}{4}$