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What is the principle value of sin-1(12)? -

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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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