Why are the Fourier Series an orthogonal basis?

Question

The Fourier Series of a function $y(x)$ is its expansion into sines and cosines:

$$y(x)= a_0+a_1\cos(x) +b_1\sin(x)+a_2\cos(2x)+b_2\sin(2x)+...$$

An Orthogonal Basis for an inner product space $V$ is a basis for $V$ whose vectors are mutually orthogonal.

For the Fourier Series example above, how do I correctly specify the orthogonal basis $B$ ?

Is it simply $B=\{\cos(x),\sin(x),\cos(2x), \sin(2x),\dots\}$?

Answer 1

Yes, together with the constant function.