Answer each of the following questions in one word or one sentence or as per exact requirement of the question: Write the difference between maximum and minimum values of sin –1 x for x ∈ [–1, 1].

Question

Philoid · Accepted Answer

Let f (x) = sin^-1 x

For x to be defined, -1 ≤ x ≤ 1

For -1 ≤ x ≤ 1, sin^-1 (-1) ≤ sin^-1 x ≤ sin^-1 (1)

⇒ -π/2 ≤ sin^-1 x ≤ π/2

⇒ -π/2 ≤ f (x) ≤ π/2

Maximum value = π/2 and minimum value = -π/2

∴ The difference between maximum and minimum values of sin^-1 x = π/2 – (-π/2) = 2π/2

= π

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:Write the difference between maximum and minimum values of sin–1x for x ∈ [–1, 1].

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the difference between maximum and minimum values of sin^–1x for x ∈ [–1, 1].