In C[0,1], with inner product defined by (3), consider the vectors 1 and x.
Find the angle theta between 1 and x.
(3)$\displaystyle \int_{0}^{1}f(x)g(x)dx$
Find the angle theta between 1 and x
You are thinking of C[0,1] as an inner product space with the standard inner product $\displaystyle <f, g>= \int_0^1 f(x)g(x)dx$.
Of course, in any inner product space, $\displaystyle <u, v>= |u||v|cos(\theta)$ where $\displaystyle \theta$ is the angle between u and v.
The particular calculation for the angle between u= 1 and v= x should be easy.