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.

Step2: Determine the quadrant of $\frac{5\pi}{6}$

The angle $\theta=\frac{5\pi}{6}$ is in the second - quadrant, where the $y$ - coordinate of a point on the unit circle is positive.

Step3: Find the value of $\sin(\frac{5\pi}{6})$

We know that for the angle $\frac{5\pi}{6}$, the coordinates of the corresponding point on the unit circle are $(-\frac{\sqrt{3}}{2},\frac{1}{2})$. So, $\sin(\frac{5\pi}{6})=\frac{1}{2}$.

Answer:

No, Josiah is not correct.