Show that the functions 1, x and cosx are orthogonal on the interval -(pi) < x < (pi) using properties of integrals of odd and even function when applicable. Given that:
f(x) = c_1 dot 1 + c_2(x) +c_3(cosx),
express c_2 in terms of integrals over the interval -(pi) < x < (pi) involving f(x) and the given functions.