Originally Posted by

**teuthid** Ok, so I keep seeing textbooks handwave over this:

Constants $\displaystyle A$,$\displaystyle B$,$\displaystyle C$, and $\displaystyle D$ exist such that

$\displaystyle A \cos{(\omega t)}+B \sin{(\omega t)}$

can be rewritten as

$\displaystyle C \cos{(\omega t -D)}$

But I haven't bee able to find/figure out the derivation of this. Can someone help me fill in the details of this?

P.S. I found one book that added $\displaystyle C=\sqrt{A^2+b^2}$ and $\displaystyle D=\tan^{-1}{(B/A)}$.