Final answer:
The exact value of sin(7π/3) is 0.
Step-by-step explanation:
To find the exact value of sin(7π/3), we can use the unit circle. First, we need to convert the angle to radians. Since π radians is equivalent to 180 degrees, we can find the equivalent angle by dividing 7π by 3. This gives us 21π/3 or 7π radians. Now, looking at the unit circle, we can see that the sine of 7π radians is equal to the y-coordinate of the point on the unit circle corresponding to that angle. In this case, since 7π is equal to three complete revolutions plus an extra π, the reference angle is π and the sine of the angle is 0. Therefore, sin(7π/3) = 0.