Question

sin^–1(sin4) =

(a) 4

(b) 4 – 2π

(c) π – 4

(d) 4 – π

Answer 1

The correct option (c) π – 4

Explanation:

4 ∈ (3 ∙ 14, 4 ∙ 71)

i.e. 4 ∈ [π, (3π/2)]

Let 4 = π + θ

∴ sin^–1(sin 4)  = sin^–1[sin(π + θ)]

= sin^–1(– sinθ)

= (– 1)θ

= – (4 – π)

= π – 4.