A point on the unit circle is \left((1)/(2), (√(3))/(2)\right). What is the sine of the angle formed by a terminal ray that intersects the unit circle at this point?

A. (1)/(2)
B. -(√(3))/(2)
C. (√(3))/(2)
D. -(1)/(2)

1 answer

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. \(\frac{\sqrt{3}}{2}\)