1. The problem statement, all variables and given/known data I read from a book (obtained from a library) which stated that: "Wave patterns, no matter how complicated, can always be written as a sum of simple wave patterns. Ex: ψ(x) = sin2x = 1/2 + cos2x/2" I understand that ψ(x) has been decomposed with double angle trignometry formulas. "More generally, it is possible to decompose the wave function into components corresponding to a constant pattern plus all possible wavelengths of hte form 2pi/n with n, an integer. That is, we can find coefficients cn such that: ψ(x) = sigma (n=0 to infinite) cn cosnx In this ex, c0 = 1/2 and c2 = -1/2. All other coefficents are zero." So...since the statement said, "wave patterns, no matter how complicated," I decided to try out with ψ(x) = sin4x out of curiosity.... 2. Relevant equations 3. The attempt at a solution ψ(x) = sin4x I used double angle formulas to get: ψ(x) = (1-cos2x)2/4...meaning the wave pattern is decomposed into: ψ(x) = 1/4 + cos2x/2 + cos22x/4 However, I am trying to figure out about "ψ(x) = sigma (n=0 to infinite) cn cosnx In this ex, c0 = 1/2 and c2 = -1/2. All other coefficents are zero." Could someone explain how to use this method so that I can try it out on ψ(x) I just made up?