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Question
What is the principle value of `sin^-1 (1/sqrt(2))`?
Options
`pi/3`
`pi/4`
`pi/5`
`pi/6`
MCQ
Solution
`pi/4`
Explanation:
Let `sin^-1 (1/sqrt(2)) = y`
Then sin `y = 1/sqrt(2)`
We know that the range of the principle value branch of `sin^-1` is `((-pi)/2, pi/2)` and `sin(pi/4) = 1/sqrt(2)`.
Therefore principle value of `sin^-1 (1/sqrt(2))` is `pi/4`.
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