Question

Evaluate each of the following:

\(sin^{-1}(sin 3)\)

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 – 3) = sin(3)

Also π–3 belongs in \([\frac{-\pi}2,\frac{\pi}2] \)

∴ sin^–1(sin3) = π–3

Answer 2

\(sin^ -1(sin-3)=0.11874839215\)