I'm having trouble seeing the equality used in Wikipedia's article on simple harmonic motion.
$c_1 \cos(\omega t) + c_2 \sin(\omega t) = A\cos(\omega t- \varphi)$
where $A = \sqrt{c_1^2 + c_2^2}$ and $\tan \varphi = c_2/c_1$, $\omega$ is a constant, and $t$ is the variable in question.