# Thread: How to calculate the Fourier series

1. ## 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

2. ## 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.