Question

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

1/2
Start Fraction 1 over 2 End Fraction

−1/2
negative Start Fraction 1 over 2 End Fraction

−√3/2
negative Start Fraction Start Root 3 End Root over 2 End Fraction

√3/2

Answer 1

In the unit circle, the coordinates of a point represent \((\cos \theta, \sin \theta)\) for some angle \(\theta\). The point \((\frac{1}{2}, \frac{\sqrt{3}}{2})\) corresponds to:

- \(\cos \theta = \frac{1}{2}\)
- \(\sin \theta = \frac{\sqrt{3}}{2}\)

The sine of the angle formed by the terminal ray that intersects the unit circle at this point is the y-coordinate of the point. Thus, the sine of the angle is:

\[
\sin \theta = \frac{\sqrt{3}}{2}
\]

So, the answer is:

\(\sqrt{3}/2\)