# Fourier Series

1. Apr 12, 2009

### fiziksfun

My professor said the Fourier series of sinx*cosx is simply 0.5sin2x.

Is this right?? Is there no summation??

I dont understand why .. Help!!

2. Apr 12, 2009

### Billy Bob

She's right, by uniqueness of Fourier series.

Trig identity for sin2x shows that sin x*cos x=0.5sin2x.

This is the form of a Fourier series, hence the unique. (All the other infinitely many terms are 0.)