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

Question

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

score 1 · Answer 1 · answered Oct 31 '15 at 18:52

1

$\cos(2\pi-\theta)=\cos(\theta)$

So clearly $\frac{11\pi}{6}=2\pi -\frac{\pi}{6}$.

Therefore $\cos(\frac{11\pi}{6})= \cos(2\pi- \frac{\pi}{6})=\cos(\frac{\pi}{6})$

answered Oct 31 '15 at 18:52

Angelo Mark

1 Answers1