Prove a set is orthogonal.

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?

tiny-tim

hi roto25! welcome to pf!

i] define the integral product

ii] define orthogonal set

iii] apply i and ii …

what do you get?

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.

chiro

Quote by 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.

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

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roto25	Prove a set is orthogonal. Tweet How would you prove, using the integral product, that the set of {cos x, cos 2x, cos 3x, cos 4x, ...} is an orthogonal set?

tiny-tim Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor	hi roto25! welcome to pf! i] define the integral product ii] define orthogonal set iii] apply i and ii … what do you get?

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.