1. The problem statement, all variables and given/known data Prove that there exists a number A>0 and \phi such that acos(ct)+bsin(ct)=Acos(ct-\phi). 2. Relevant equations a,b,c are predermined constants where c>0. From this equation I can justify conclusions regarding the amplitude, frequency, and so forth of a simple harmonic ocillator. 3. The attempt at a solution Obviously if a (or b) is 0, then A is equal b (or a, respectively) and \phi is 0. Thus, I can now assume that a and b are not 0. I try defining two different functions and proving that they are equal for every t using properties of the derivatives.