Question

click the arrows to choose an answer from each menu. the y - coordinate of the endpoint of the terminal side is choose.... on the unit circle are choose.... so sin(5π/6)= choose.... the coordinates of any point. josiah choose....

Explanation:

Step1: Recall unit - circle properties

On the unit circle \(x^{2}+y^{2}=1\), for an angle \(\theta\), the coordinates of the terminal - side endpoint are \((\cos\theta,\sin\theta)\).

Step2: Evaluate \(\sin(\frac{5\pi}{6})\)

We know that \(\frac{5\pi}{6}\) is in the second - quadrant. The reference angle \(\theta_{r}=\pi-\frac{5\pi}{6}=\frac{\pi}{6}\). And \(\sin\) is positive in the second - quadrant. Since \(\sin(\frac{\pi}{6})=\frac{1}{2}\), then \(\sin(\frac{5\pi}{6})=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)