Final answer:
The exact value of sin(-3π/2) is -1.
Step-by-step explanation:
The exact value of the trigonometric function sin(-3π/2) is -1.
To find this value, we need to determine the value of sin(-3π/2), which represents the sine function evaluated at an angle of -3π/2 radians. Since the sine function has a period of 2π, we can subtract 2π from -3π/2 to get an equivalent angle within one period. -3π/2 - 2π = -7π/2.
The sine function has a value of -1 at -π/2, and since -7π/2 is an additional 6 periods away, the value of sin(-3π/2) is also -1.