What is the exact value of arcsin (-√3/2)

Arcsine of a value like y is the inverse of that value y.

Lets take that,

arcsin (-√3/2) = Ф then,

sin Ф = - √3/2

For a right triangle with length 1 and base √3, has a hypotenuse of 2.

This gives us,

sin 30° = √3/2

∴ sin - 30° = - √3/2

This now means that arcsin (-√3/2) = - 30.

But since we measure angles in anticlockwise direction, - 30° = 330° and 210°.

Answer: arcsin (-√3/2) = 210° and 330° for angles below 360°.