Prove a set is orthogonal.

1. Apr 3, 2012

roto25

How would you prove, using the integral product, that the set of {cos x, cos 2x, cos 3x, cos 4x, ...} is an orthogonal set?

Last edited: Apr 4, 2012
2. Apr 4, 2012

tiny-tim

welcome to pf!

hi roto25! welcome to pf!

i] define the integral product

ii] define orthogonal set

iii] apply i and ii …

what do you get?

3. Apr 5, 2012

Bavid

over the interval -pi to pi, the integral of cos(mx)cos(nx)dx is zero, as long as m and n are integers. Therefore, if you select ANY pair of elements from the set, the 'integral of their product' will be zero, thereby satisfying the condition of orthogonality.

4. Apr 5, 2012

chiro

On top of what Bavid said if you don't know where to start set up the integral and use integration by parts.