The coordinates of the point on the unit circle are given as \(\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)\). In the context of the unit circle, the x-coordinate represents the cosine of the angle, and the y-coordinate represents the sine of the angle.
From the point \(\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)\):
- The x-coordinate (cosine) is \(\cos(\theta) = \frac{1}{2}\).
- The y-coordinate (sine) is \(\sin(\theta) = \frac{\sqrt{3}}{2}\).
Therefore, the sine of the angle formed by the terminal ray that intersects the unit circle at this point is:
\[ \sin(\theta) = \frac{\sqrt{3}}{2} \]
The correct answer is:
C. \(\frac{\sqrt{3}}{2}\)