Solution
= Solution
Use the real <inner product>
$$
\langle f,g\rangle=\int_{-L}^{L}f(x)g(x)\,dx.
$$
<Orthogonality> means this <integral> is zero for any two distinct listed <functions>. The individual squared <norms> are positive: the constant function has squared <norm> $2L$, while every listed <sine> or <cosine> has squared <norm> $L$. Thus they are orthogonal but not normalized to unit length in this <inner product>.