Deriving a polynomial equation from a data set of 360 points using the Lagrange Method

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I have a data set of 360 points, where on the x-axis I have every day of the year. On the y-axis, I have a set of integer values of the same length. I want to use the Lagrange Method to derive a polynomial equation from the data set, however this means the polynomial would end up in the 359th degree -- a very large exponent. Would it make more sense to take a subset of these points to derive the equation? And if I did, would it still accomplish my goal?