Question

Write the difference between maximum and minimum values of  sin⁻¹ x for x ∈ [− 1, 1].

Answer 1

The maximum value of `sin^-1x` in x ∈ [− 1, 1] is at 1.
So, the maximum value is

`sin^-1(1)`

`=sin^-1(sin  pi/2)`

`=pi/2`

Again, the minimum value is at -1.
Thus, the minimum value is

`sin^-1(-1)=-sin^-1(1)`

`=-sin^-1(pi/2)`

`=-pi/2`

So, the difference between the maximum and the minimum value is `pi/2-(-pi/2)=pi`