Question

Find the exact value of the real number y when y = arcsin(-√3/2).

a) -π/3
b) -π/4
c) -π/6
d) -π/2

Answer 1

The exact value of y for y = arc sin(-√3/2) is -π/3, which corresponds to option a) -π/3 in the given options.

Step-by-step explanation:

To find the exact value of the real number y when y = arc sin(-√3/2), we consider the sine function and the corresponding angles whose sine gives -√3/2. The sine function has a value of -√3/2 at an angle of -π/3 in the unit circle.

This is because the sine of π/3 is √3/2, and taking the negative of this value mirrors the angle from the first quadrant to the fourth quadrant, where it remains within the range of arc sin, between -π/2 and π/2.

The correct option that represents this value is option a) -π/3.

Hence, y = -π/3 is the solution when solving this mathematical problem completely.