How to find trigonometric function from a list of points?

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I am trying to find a way to model a trigonometric/other function to fit the points that can be found in the photograph. The aim is to turn this function into a polar equation to model the shape of an object.

Some people have recommended the use of Fourier Transform/Taylor approximations, but both require a function to begin with. The aim here is to find one function to model the entire curve, so while splitting it up into a piecewise function may be an intuitive way, I'm keeping it as a last resort.

Image of points can be found here