First of all, I apologize for my English. I'm Spanish, so I hope you can all understand me.
Here is my problem. Given the inner product:
$$ \int_0^\pi f(x)g(x)dx\ $$
in the space of continuos real valued functions, I have to calculate the angle between the vectors $ \sin(x) $ and $ \cos(x) $.
I know the formula, that is a consequence of the Cauchy–Schwarz inequality, but I am having trouble calculating the norm of the vectors.
Also, is this angle unique or varies according to the inner product? And what about the norm of a vector? Why?