#### 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/2) = - 1/2`

Therefore, the principal value of `sin^(-1) (-1/2) is - pi/6`

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Solution Find the Principal Values of Sin^(-1) (-1/2) Concept: Basic Concepts of Trigonometric Functions.