Question

How do you find `arcsin(-sqrt3/2)` without a calculator?

Answer 1

First way: Use the Trig Table of Special Arcs
`sin x = (-sqrt3/2)` --> arc x = -60 deg and arc x = -120 deg.

Second way: Use the trig unit circle.
In the triangle OMm, angle M = 60 deg ; OM = 1 unit ; Mm = 1/2.

Therefor,`(Om)^2 = 1 - 1/4 = 3/4` --> `Om = sqrt3/2`

sin (-60) = sin (-120) = - `sqrt3/2`

Answer 2

240

Explanation:

Since the value of the sine is negative, it should be in the third quadrant.

As we know `Sin (π/3) = sqrt(3)/2`
Hence `sin^-1(-sqrt(3)/2) = (π+π/3)`
Hence, `Arcsin (-sqrt(3)/2) = 4π/3`
In degrees, take π radians = 180 degrees.
Hence `Arcsin (-sqrt(3)/2)= 240 degrees`