Math Help - Finding the norm and scalar product of sin(aX),cos(bX) in the vector space C(0,Pi)

1. Finding the norm and scalar product of sin(aX),cos(bX) in the vector space C(0,Pi)

Hi im trying to calculate the norm and scaler product of sin ax and cos bx in vector space C(0,Pi) . i think the solution might be to projection but im not entirely sure how to do it.

2. Originally Posted by partickrock
Hi im trying to calculate the norm and scaler product of sin ax and cos bx in vector space C(0,Pi) . i think the solution might be to projection but im not entirely sure how to do it.
A vector space as such does not have a norm or inner (scalar) product.

The usual inner product on the space of continuous real functions on a closed interval $[a,b]$ is:

$\langle a,b \rangle =\int_a^b a(x)b(x) \ dx$

CB