trig help for inverse sin

Question

how do I solve, please explain:

sin^-1 -√3 / 2

The answer is -¶/3 but I don't understand why.

Thank you

Answer 1

Inverse sine in x = sin^-1 (-√3 /2) reads as follows: x is the angle whose sine value is -√3 /2. Looking at the Unit Circle, one place this occurs (not the only) is at 5π/3, which is below the positive x axis that represents both zero and 2π radians. With 2π = 6π/3 obviously, angle x can be expressed as 5π/3 - 6π/3 = -π/3.