4. Let C[0, 27) denote the real vector space of all continuous functions f:[0,21] + R, equipped with the inner product (f,g) = | f(x)g(x)dx. (a) (1 point) Show that for any non-negative integers m # n, the functions sin(nx) and sin(mx) are all mutually orthogonal. (b) (2 points) Fix a natural number N, and find the function fn in span(sin(nx) | 0 <>