Find the exact real value of arcsin. the quantity square root of three divided by two. (-√3/2)?

Solution:

Given, arcsin(-√3/2)

arcsin(-√3/2) is the angle whose sine is -√3/2.

As sine is negative in third quadrant and fourth quadrant

sin(π/3) = √3/2,

we have sin(π - π/3) = -√3/2.

sin(π + π/3) = -√3/2

arcsin(-√3/2) = 2π/3 or 4π/3

Adding or subtracting 2π does not affect trigonometric ratios of angles as they are all coterminal angles.

We can have infinite solutions given by

(2n + 1)π ± π/3, where n is an integer.

Therefore, the exact real value of arcsin is -π/3.

Find the exact real value of arcsin. the quantity square root of three divided by two. (-√3/2)?

Summary:

The exact real value of arcsin the quantity square root of three divided by two (-√3/2) is -π/3.