# Orthogonality of Sine and Cosine functions

1. Jun 10, 2009

### Hendrick

Hi,

would anyone be able to explain how to evaluate a function using orthogonality (i.e. using orthogonality to solve a definite integration problem with sines/cosines)?

Thank you

2. Jun 10, 2009

### ExactlySolved

3. Jun 11, 2009

### daviddoria

Orthogonality in a vector space means that the inner product of two vectors is 0. In this case, your space is a function space so the inner product is defined as the integral of the product of the functions.

http://en.wikipedia.org/wiki/Orthogonal#Orthogonal_functions

4. Jun 12, 2009

### Bob S

I would look in (already referenced in post #2 By ExactlySolved)
http://mathworld.wolfram.com/FourierSeries.html
And in particular look at Eqns (8) and (9) for solving for the coefficients in a Fourier series. Also look at (18) and (19). The sine-like and cosine-like terms are orthogonal, as proved by integrating their product over the interval 0 to 2 pi.