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Question
Find the principal values of `sin^(-1) (-1/2)`
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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