Finding a basis from inner product

[heartshapes]

An inner product on the space of continuous functions on the interval [0,?] is given by < f(x),g(x)> = ?f(x)g(x)dx.
Find a basis for the members of H = span{1, sin(x)} that are orthogonal to the constant functions.

So the first thing that I am lost on is what does H = span{1,sin(x)} mean.. does it mean it's the set whenever 1 = sin(x). like ?/2?
Then how do I apply that to the constant functions of the inner product?
Any help would be greatly appreciated.

 

[tkhunny]

H = span{1, sin(x)} means the collection of all functions that can be created from linear combinations of '1' and 'sin(x)'

Can you perform Gramm-Schmidt Orthoginalization? With only two functions int he basis, it should not take long.