Answer 1

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`