Evaluate each of the following:\(sin^{-1}(sin 3)\)

1.	Evaluate each of the following:\(sin^{-1}(sin 3)\)
Answer» 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 \(sin^ -1(sin-3)=0.11874839215\)

Answer»

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

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

Discussion