Question

What is the value of `sin^-1(sin  (3pi)/4)`?

पर्याय

• `pi/5`

• `(2pi)/5`

• `(5pi)/2`

• `pi/2`

Answer 1

`(2pi)/5`

Explanation:

We know that sin^–1 (sin x) = x

Therefore `sin^-1 (sin  (3pi)/5) = (3pi)/5`

But `(3pi)/5 ∉ [- pi/2, pi/2]`, Which is the principle branch of sin^–1x.

However, `sin((3pi)/5) = sin(pi - (3pi)/5) = sin  (2pi)/5` and `(2pi)/5 ∉ [- pi/2, pi/2]`

Therefore `sin^-1(sin  (3pi)/5) = sin^-1 (sin  (2pi)/5) = (2pi)/5`.