To find the coordinates of the point where the terminal side of a 120-degree angle intersects the unit circle, we start by understanding that the unit circle has a radius of 1.
The angle of 120 degrees is in the second quadrant. In the unit circle, the coordinates can be found using the cosine and sine functions:
- Cosine of the angle:
cos(120°) = -1/2 - Sine of the angle:
sin(120°) = √3/2
Thus, the coordinates where the terminal side intersects the unit circle are:
(cos(120°), sin(120°)) = (-1/2, √3/2)
Looking at the provided answer choices:
- a) 1, 2√3/2
- b) 1, 2√3/2
- c) √3/2, 1/2
- d) 1, 2√3/2
None of the choices accurately represent the coordinates (-1/2, √3/2). However, if we consider the absolute values and orientation with respect to the unit circle, the coordinates we found are (-1/2, √3/2). Therefore, it appears there may be an error in the answer choices provided.