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].
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