Question about fitting periodic data

[ftft]

My experience with data fitting is poor so I am in real need for help.
The potential in the following is periodic over [0,Pi]

I need to find a fitting function that I can use to perform further mathematics. Fourier series does not work, but a 40-degree polynomial give the following fit

However, the polynomial does not preserve its periodicity over the cycle. Could someone please advice what I should do to get a good fitting function for my data?

 

[micromass]

Fitting with a polynomial with degree larger than 3 is a really bad idea.

Why don't you try to fit this function with a combination of straight lines?? And why do Fourier series not work?

 

[mfb]

A set of straight lines for different ranges should fit best. A Fourier series should give reasonable approximations, but only if you include many terms.

 

[Svein]

Looking at the vertical scale: Is your data set really constricted to the value -9.74771?