find the exact value.\ncos(5π/6)\ntype + or -\n?√/

Explanation:

Step1: Rewrite the angle

We know that $\frac{5\pi}{6}=\pi-\frac{\pi}{6}$. Then $\cos\frac{5\pi}{6}=\cos(\pi - \frac{\pi}{6})$.

Step2: Apply the cosine - difference formula

The formula $\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = \pi$ and $B=\frac{\pi}{6}$. So $\cos(\pi-\frac{\pi}{6})=\cos\pi\cos\frac{\pi}{6}+\sin\pi\sin\frac{\pi}{6}$. Since $\cos\pi=- 1$, $\sin\pi = 0$, and $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$, $\sin\frac{\pi}{6}=\frac{1}{2}$, we have $\cos(\pi-\frac{\pi}{6})=(-1)\times\frac{\sqrt{3}}{2}+0\times\frac{1}{2}=-\frac{\sqrt{3}}{2}$.

Answer:

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