Final Answer:
-π/3 is located in Quadrant IV on the unit circle.
Thus option d is correct.
Step-by-step explanation:
The unit circle is a circle centered at the origin with a radius of 1 unit. The angles measured counterclockwise from the positive x-axis on the unit circle. In this case, -π/3 is equivalent to a rotation of 60 degrees clockwise from the positive x-axis (since -π/3 is the negative equivalent of π/3). To determine its location, start from the positive x-axis (0 degrees) and rotate clockwise by 60 degrees. This brings you to the lower right-hand side of the unit circle, falling into Quadrant IV.
Using the reference of 60 degrees, consider the coordinates on the unit circle. At 60 degrees (or π/3), the coordinates are (cos(π/3), sin(π/3)). For -π/3, which is in Quadrant IV, the x-coordinate (cosine) will remain positive as it moves to the right, while the y-coordinate (sine) will be negative as it moves downward. Therefore, the coordinates for -π/3 are (cos(-π/3), sin(-π/3)) = (cos(π/3), -sin(π/3)) = (1/2, -√3/2), placing it in Quadrant IV.
In conclusion, the angle -π/3 on the unit circle falls into Quadrant IV, indicated by the coordinates (1/2, -√3/2), as it corresponds to a 60-degree clockwise rotation from the positive x-axis.
Therefore option d is correct.