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Question
Find the principal value of the following:
`sin^(-1) (-1/2)`
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Solution
Let `sin^(-1) (-1/2)` = y
Then sin y = `-1/2 = -sin(pi/6) = sin(-pi/6)`
We know that the range of the principal value branch of sin−1 is
`[-pi/2, pi/2]` and `sin (-pi/6) = - 1/2,`
Where `-pi/6 ∈ [-pi/2,pi/2]`
Therefore, the principal value of `sin^(-1) (-1/2)` is `-pi/6`.
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