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

based on the unit circle shown, josiah claims that sin(5π/6)= -√3/2. is josiah correct? use the drop - down menus to explain. click the arrows to choose an answer from each menu. the y - coordinate of the endpoint of the terminal side is choose. the coordinates of any point on the unit circle are choose, so sin(5π/6)= choose. josiah choose correct

based on the unit circle shown, josiah claims that sin(5π/6)= -√3/2. is josiah correct? use the drop - down menus to explain. click the arrows to choose an answer from each menu. the y - coordinate of the endpoint of the terminal side is choose. the coordinates of any point on the unit circle are choose, so sin(5π/6)= choose. josiah choose correct

Answer

Explanation:

Step1: Recall unit - circle definition

For a unit - circle (x^{2}+y^{2}=1), and for an angle (\theta), the coordinates of the point on the unit - circle are ((\cos\theta,\sin\theta)).

Step2: Identify the angle

We have (\theta=\frac{5\pi}{6}). The (x) - coordinate of the point on the unit - circle for (\theta = \frac{5\pi}{6}) is (x = \cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}), and we use the equation of the unit - circle (x^{2}+y^{2}=1) to find the (y) - coordinate. Substitute (x = -\frac{\sqrt{3}}{2}) into (x^{2}+y^{2}=1): (\left(-\frac{\sqrt{3}}{2}\right)^{2}+y^{2}=1), which simplifies to (\frac{3}{4}+y^{2}=1), then (y^{2}=1 - \frac{3}{4}=\frac{1}{4}), so (y=\frac{1}{2}) (since the angle (\frac{5\pi}{6}) is in the second quadrant where (y>0)).

Step3: Determine the sine value

Since for a point ((x,y)) on the unit - circle corresponding to an angle (\theta), (\sin\theta=y), for (\theta=\frac{5\pi}{6}), (\sin\frac{5\pi}{6}=\frac{1}{2}).

Answer:

The (y) - coordinate of the endpoint of the terminal side is (\frac{1}{2}). The coordinates of any point on the unit - circle are ((\cos\theta,\sin\theta)), so (\sin\left(\frac{5\pi}{6}\right)=\frac{1}{2}). Josiah is not correct.