Final answer:
The exact real value of arcsin(-√3/2) is 4π/3 radians or 240 degrees, which corresponds to an angle in the third quadrant where sine is negative.
Step-by-step explanation:
The student's question relates to finding the exact real value of the inverse sine function, also known as arcsin, when given a specific value. To find arcsin(-√3/2), we need to recall our unit circle and the values of sine that correspond to different angles. The sine of a certain angle is √3/2 at 120 degrees or π/3 radians, and the sine of an angle is -√3/2 at 240 degrees or 4π/3 radians.
Since the value is negative (-√3/2), we're looking for the angle in the third or fourth quadrant where sine values are negative. The exact real value of arcsin(-√3/2) is therefore 4π/3 radians, or 240 degrees.