I was working on compound angles formula problems, when I encountered this problem:
$\sin\left(\frac{5\pi}{9}\right)$
$\cos\left(\frac{7\pi}{18}\right)$
I know how to use the formula, but I'm not sure how to break up these two angles into simplified angles in order to calculate the value without a calculator .
Hint: $\frac{5\pi}{9}=\frac{10\pi}{18}$, so $$\frac{5\pi}{9}-\frac{7\pi}{18}=\frac{3\pi}{18}=\frac{\pi}{6}.$$