Easy: If the function is even then a cosine series will do, and if it is odd a sine series will do. This is just to say that for an even function all sine coefficients will be zero, and for an odd function all cosine coefficients will be zero.
Easy: If the function is even then a cosine series will do, and if it is odd a sine series will do. This is just to say that for an even function all sine coefficients will be zero, and for an odd function all cosine coefficients will be zero.