Question

Evaluate each of the following:

sin^-1(sin 2)

Answer 1

sin^–1(sin x) = x

Provided x ∈\([\frac{-\pi}2,\frac{\pi}2] \) ≈ [–1.57,1.57] 

And in our equation x is 3 which does not lie in the above range.

We know sin[π – x] = sin[x]

∴ sin(π – 2) = sin(2)

Also π–2 belongs in \([\frac{-\pi}2,\frac{\pi}2] \)

∴ sin^–1(sin2) = π–2