Question

what is cos \frac{11\pi}{6}?

Explanation:

Step1: Convert the angle

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

Step2: Use the cosine subtraction formula

$\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = 2\pi$, $B=\frac{\pi}{6}$. Since $\cos(2\pi)=1$ and $\sin(2\pi)=0$, then $\cos(\frac{11\pi}{6})=\cos(2\pi-\frac{\pi}{6})=\cos(2\pi)\cos(\frac{\pi}{6})+\sin(2\pi)\sin(\frac{\pi}{6})$.
Substituting the values: $\cos(\frac{11\pi}{6})=1\times\frac{\sqrt{3}}{2}+0\times\frac{1}{2}=\frac{\sqrt{3}}{2}$

Answer:

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