# Using the compound-angle formula, determine the exact value.

I understand how to use the compound angle formula on fractions with a numerator less than the denominator such as

$$\sin\left(\frac{5\pi}{12}\right) = \sin\left(\frac{\pi}{4} +\frac{\pi}{6}\right)$$

However Im having trouble when the numerator is greater. Could someone please assist me with $\cos\left(\frac{11\pi}{6}\right)$

• You can use $2\pi$ and $\frac{\pi}{6}$ , if you consider $cos(x-y)=cos(x+(-y))$ and $cos(-y)=cos(y)$ , $sin(-y)=-sin(y)$ – Peter Oct 31 '15 at 18:50
• ${11 \pi \over 6} = 2 \pi - {1 \pi \over 6}$. – copper.hat Oct 31 '15 at 18:51
• You mean $11/6=1+5/6$? or something deeper? – Lubin Oct 31 '15 at 18:51
• @Laura Welcome to math stack exchange! – Peter Oct 31 '15 at 18:54
• This particular problem is just screaming for a diagram. – John Joy Oct 31 '15 at 19:48

$\cos(2\pi-\theta)=\cos(\theta)$
So clearly $\frac{11\pi}{6}=2\pi -\frac{\pi}{6}$.
Therefore $\cos(\frac{11\pi}{6})= \cos(2\pi- \frac{\pi}{6})=\cos(\frac{\pi}{6})$