Orthogonality of Sine and Cosine functions

  • Thread starter Hendrick
  • Start date
  • #1
43
0
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
 

Answers and Replies

  • #3
97
0
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
4,662
6
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.
 

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