Sinusodial Regression by hand to model data points

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I'm currently working on an assignment, where I am attempting to model COVID-19 cases using sinusoidal regression. I need to create my model by hand and would appreciate any help possible. I've done quite a bit of research online, but all I have found are instructions to have the TI 84 complete this procedure.

I want to model my data using the equation: =*sin(+)+

Data: Part 1

Part 2

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The fitting is very bad with the model equation $y=A\:\sin(B_:x+C)+D$.

It can be a little improved with the model equation below. But the fitting remains not good. The scatter is too large and the patern isn't enough regularly repetitive like in a function of sinusoidal kind.

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