Question

no calculator is allowed on this question.
an angle measuring \\(\frac{2\pi}{3}\\) radians is in standard position and intersects the unit circle at point \\(s\\). if \\(\sin \frac{2\pi}{3} = \frac{\sqrt{3}}{2}\\) and \\(\cos \frac{2\pi}{3} = -\frac{1}{2}\\), what is the \\(y\\)-coordinate of point \\(s\\)?
select one answer
a \\(-\frac{\sqrt{3}}{2}\\)
b \\(-\frac{1}{2}\\)
c \\(\frac{1}{2}\\)
d \\(\frac{\sqrt{3}}{2}\\)

Explanation:

Step1: Recall unit circle coordinates

For an angle \(\theta\) in standard position intersecting the unit circle at \((x,y)\), \(x = \cos\theta\) and \(y=\sin\theta\).

Step2: Identify \(y\)-coordinate

Given \(\theta=\frac{2\pi}{3}\), and \(\sin\frac{2\pi}{3}=\frac{\sqrt{3}}{2}\), so the \(y\)-coordinate of point \(S\) is \(\sin\frac{2\pi}{3}\).

Answer:

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