Let f(x)=sinx, g(x)=sqrt(1-x^2). Find (fog)(x) and (gof)(x) and their domain.

Well I can answer (fog)(x) and (gof)(x), which are sin[sqrt(1-x^2)], and [sqrt(1-sinx^2)] respectively. However, I dont know how to find the domain. Any help would be appreciated. Thanks