Periodic Solutions to f(x)^2 + g(x)^2 = 1: Generalized Sine and Cosine Functions Ronald Mickens Clark Atlanta University Physics We discuss the periodic solutions to the functional equation f(x)^2 + g(x)^2 = 1 and show that they have essentially the same mathematical properties as the trigonometric sine and cosine functions. An interesting and very important result is that in addition to the periodic functions f(x) and g(x), there must also exist a third periodic function, d(x).