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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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