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What is the value of sin-1(sin 3π4)? -

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Question

What is the value of `sin^-1(sin  (3pi)/4)`?

Options

  • `pi/5`

  • `(2pi)/5`

  • `(5pi)/2`

  • `pi/2`

MCQ

Solution

`(2pi)/5`

Explanation:

We know that sin–1 (sin x) = x

Therefore `sin^-1 (sin  (3pi)/5) = (3pi)/5`

But `(3pi)/5 ∉ [- pi/2, pi/2]`, Which is the principle branch of sin–1x.

However, `sin((3pi)/5) = sin(pi - (3pi)/5) = sin  (2pi)/5` and `(2pi)/5 ∉ [- pi/2, pi/2]`

Therefore `sin^-1(sin  (3pi)/5) = sin^-1 (sin  (2pi)/5) = (2pi)/5`.

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