1. The problem statement, all variables and given/known data Hello, I found this problem in the book I borrowed from the library, but this book does not have solutions in the back....I tried to lent the solution book but the library does not have it...so could someone help me out? The question is: It is possible to decompose the function f(x) into components corresponding to a constant pattern plus all possible functions of the form 2pi/n with n as integer. Again, by this, supposing: f(x) = sin2x = 1/2 + cos2x/2 --> f(x) = Sigma (n= 0 to infinite) cn cosnx...in this example, c0 = 1/2 and c2 = -1/2, where ALL other coefficients are zero. So, based on the example, expand and find co-efficients for f(x) = sin4x by using double angle formulas, and then EXPLAIN why only even values of n show up. I already figured out the first part of the question, and i am pretty sure I am right. But, I have no idea about the "Explain" part... 2. Relevant equations posted above 3. The attempt at a solution I figured out the expansion and already found co-efficients for f(x) = sin4x, which is: f(x) = 3/8 - cos2x/2 + cos4x/8 by using double angle formula twice, sin2x and cos2x: c0 = 3/8 c2 = -1/2 c4 = 1/8 ...so I suppose all other coefficients are zero? Also, I still do not understand about "Explain why only even values of n show up?" Could someone help?