Question

sketch θ = - 5π/6 radians in standard position on the unit - circle. find the lengths of the legs of its reference triangle. these are labeled a and b in the figure below, when an angle is sketched. then use your reference triangle to find the coordinates of point p. use exact values and not decimal approximations. a = b = p=( )

Explanation:

Step1: Analyze the angle position

The angle $\theta =-\frac{5\pi}{6}$ is in the third - quadrant. Its reference angle $\theta_{r}=\frac{\pi}{6}$.

Step2: Recall trigonometric relationships on unit - circle

For a point $P=(a,b)$ on the unit - circle $x = a=\cos\theta$ and $y = b=\sin\theta$. For $\theta=-\frac{5\pi}{6}$, we know that $\cos(-\frac{5\pi}{6})=-\frac{\sqrt{3}}{2}$ and $\sin(-\frac{5\pi}{6})=-\frac{1}{2}$.

Answer:

$a =-\frac{\sqrt{3}}{2}$, $b =-\frac{1}{2}$, $P=(-\frac{\sqrt{3}}{2},-\frac{1}{2})$