Question

based on the unit circle shown, josiah claims that sin(5π/6)= -√3/2. is josiah correct? use the drop - down menus to explain.

Explanation:

Step1: Recall sine - unit circle relationship

On the unit circle, for an angle $\theta$, $\sin\theta$ is the $y$ - coordinate of the point where the terminal side of the angle intersects the unit circle.
The angle $\theta=\frac{5\pi}{6}$ is in the second - quadrant.

Step2: Determine the sign of sine value

In the second - quadrant, the $y$ - coordinates of points on the unit circle are positive.
The reference angle for $\theta = \frac{5\pi}{6}$ is $\pi-\frac{5\pi}{6}=\frac{\pi}{6}$.
We know that $\sin\frac{\pi}{6}=\frac{1}{2}$ and for $\theta=\frac{5\pi}{6}$, $\sin\frac{5\pi}{6}=\frac{1}{2}$.

Step3: Evaluate Josiah's claim

Josiah claims that $\sin(\frac{5\pi}{6})=-\frac{\sqrt{3}}{2}$, which is incorrect.

Answer:

No, Josiah is not correct.