Polynomial and Trigonometric Function Optimum Fitting

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I am going to do optimum fitting for data on mu-slip characterization of a vehicle on dry asphalt surface at 40 miles/hr using polynomial characterization optimum fitting for problem 1 and trigonometric function characterization optimum fitting for problem 2. I am not sure how to get started. Can anyone help me on this? Attached is my HW assignment.

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