# How to calculate the Fourier series

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• May 10th 2013, 01:56 AM
Brennox
How to calculate the Fourier series
so f(x) = 2sin(t)cos(t)

it has odd symertry, -f(x) = f(-x). but i dont know how relevent this is
• May 10th 2013, 07:25 AM
HallsofIvy
Re: How to calculate the Fourier series
I presume you know the basic formulas?
The coefficient of "cos(nx)" is $a_n= \frac{1}{\pi}\int_{-\pi}^\pi (2 sin(t)cos(t))cos(nt)dt$
The coefficient of "sin(nx)" is $b_n= \frac{1}{\pi}\int_{-\pi}^\pi (2sin(t)cos(t) sin(nt)dt$

Because 2sin(t)cos(t) is an odd function, its Fourier series includes only odd terms- that is no cos(nx) term. $a_n= 0$ for all n.