Consider functions of the form $\displaystyle h(x) = f(x)+g(x)$, where f and g are sine and/or cosine functions with the same amplitude. How do the periods of g and g determine the period of h?

I have to draw a conclusion about the relationship between the period of h(x) = f(x)+g(x) and the periods of f and g. The only thing I can figure out is that the period of a sine function is $\displaystyle \frac{2\pi}{c}$ when $\displaystyle f(x)=sin(cx)$.