Evaluate each of the following:sin-1(sin 12)

1.	Evaluate each of the following:sin-1(sin 12)
Answer» sin^–1(sin x) = x Provided x ∈\([\frac{-\pi}2,\frac{\pi}2]\)≈ [–1.57,1.57] And in our equation x is 4 which does not lie in the above range. We know sin[2nπ – x] = sin[–x] ∴ sin(2nπ – 12) = sin(–12) Here n = 2 Also 2π–12 belongs in \([\frac{-\pi}2,\frac{\pi}2]\) ∴ sin^–1(sin12) = 2π – 12

Answer»

sin^–1(sin x) = x

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

And in our equation x is 4 which does not lie in the above range.

We know sin[2nπ – x] = sin[–x]

∴ sin(2nπ – 12) = sin(–12)

Here n = 2

Also 2π–12 belongs in \([\frac{-\pi}2,\frac{\pi}2]\)

∴ sin^–1(sin12) = 2π – 12

Discussion