Originally Posted by

**myoplex11** I have a question.

Find the Fourier series if f(x) of period 2L and write the first three terms.

f(x) = { sinx , 0 < x < pi

0 , -pi < x < 0

When the function is broken up into even and odd functions

f(x) = 0.5*sinx + 0.5*|sinx|

the resulting f(x) comes out

f(x) = 1/pi + 0.5*sinx - 2/pi[(cos2x)/3 + (cos4x)/15 + (cos6x)/35]

But when the function is worked out without splitting it up, the resulting f(x) comes out

f(x) = 1/pi - 2/pi[(cos2x)/3 + (cos4x)/15 + (cos6x)/35]

So my question to you is this, where does the "0.5*sinx" come from in the first answer and why don't the two answers equal one another?