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

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