Final answer:
The exact value of sin (-π/2) is found based on its location on the unit circle, and the value is -1.
Step-by-step explanation:
The student has asked to find the exact value of the sine function at the given real number, which is sin (-π/2).
To determine the value, we can recall the unit circle, where the sine of an angle corresponds to the y-coordinate of the point where the terminal side of the angle intersects the unit circle. For π/2, or 90 degrees, the point on the unit circle is (0, 1), so sin (π/2) = 1.
However, the negative sign in front of π/2 indicates that the angle measurement is in the negative direction, which is clockwise from the positive y-axis. So, sin (-π/2) corresponds to the point (0, -1) on the unit circle. Therefore, the exact value of sin (-π/2) is -1.