Inverse Trigonometric Functions

Question

please explain this to me in mathematical steps please

how to solve sin^(-1) (-1/2)
this equals - pi/6

i know that sin^(-1) domain and range switch from original sin

but i don't know how to apply that... i need an mathematical explanation or if that isn't possible please explain it as simply as possible

thank you in advance

Answer 1

i want to know how it equals -pi/6