What do I do when I have an equation such as cos(3x)=0.5 ? I can't use double angle identities so I was wondering if there are some identities that I am missing?
Just solve the equation directly...
$\displaystyle \displaystyle \begin{align*} \cos{(3x)} &= \frac{1}{2} \\ 3x &= \left\{ \frac{\pi}{3}, \frac{5\pi}{3} \right\} + 2\pi\, n \textrm{ where } n \in \mathbf{Z} \\ x &= \left\{ \frac{\pi}{9}, \frac{5\pi}{9} \right\} + \frac{2\pi}{3}\, n \end{align*}$