find the exact value. cos 11π/6 type + or - ? √ /

Answer:

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

Explanation:

Step1: Rewrite the angle

$\frac{11\pi}{6}=2\pi-\frac{\pi}{6}$

Step2: Use cosine property

$\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = 2\pi$, $B=\frac{\pi}{6}$. Since $\cos(2\pi)=1$ and $\sin(2\pi)=0$, then $\cos(\frac{11\pi}{6})=\cos(2\pi-\frac{\pi}{6})=\cos(2\pi)\cos(\frac{\pi}{6})+\sin(2\pi)\sin(\frac{\pi}{6})$.

Step3: Substitute values

We know that $\cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}$ and $\sin(\frac{\pi}{6})=\frac{1}{2}$, $\cos(2\pi) = 1$, $\sin(2\pi)=0$. So $\cos(\frac{11\pi}{6})=1\times\frac{\sqrt{3}}{2}+0\times\frac{1}{2}=\frac{\sqrt{3}}{2}$.