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