what is the value of cos (π/3)? √3/2 1/2 -1/2 -√3/2

Explanation:

Step1: Recall the unit - circle values

We know that $\frac{5\pi}{6}=150^{\circ}$ in degree measure. On the unit - circle, for an angle $\theta = 150^{\circ}$, the cosine value is the $x$ - coordinate of the point on the unit - circle corresponding to this angle. We also know the reference angle for $150^{\circ}$ is $180^{\circ}-150^{\circ} = 30^{\circ}$.

Step2: Determine the sign and value

In the second quadrant, the cosine function is negative. And $\cos(30^{\circ})=\frac{\sqrt{3}}{2}$. So, $\cos(150^{\circ})=-\frac{\sqrt{3}}{2}$. Since $\frac{5\pi}{6}=150^{\circ}$, then $\cos(\frac{5\pi}{6})=-\frac{\sqrt{3}}{2}$.

Answer:

$-\frac{\sqrt{3}}{2}$