Question

What is the principle value of `sin^-1 (1/sqrt(2))`?

पर्याय

• `pi/3`

• `pi/4`

• `pi/5`

• `pi/6`

Answer 1

`pi/4`

Explanation:

Let `sin^-1 (1/sqrt(2)) = y`

Then sin `y = 1/sqrt(2)`

We know that the range of the principle value branch of `sin^-1` is `((-pi)/2, pi/2)` and `sin(pi/4) = 1/sqrt(2)`.

Therefore principle value of `sin^-1 (1/sqrt(2))` is `pi/4`.