@AntoniParellada so in order to get the number of fourier terms, I used an arima model to obtain that. Whichever amount of K-terms produced the lowest AIC is what I went with. For the seasonality portion specifically though, would just the RowSum of my current output in the question work? - just for seasonality

Just to confirm, if I wanted to extract the seasonality, do I just take the rowsums of my output I provided in the original question?

Thanks! That's really interesting how that works. Regardless of the actual data, you will always get the same harmonics. It all really depends when you do an auto.arima() with the actual sales data to optimally choose the number of K-values. You can see which arima model produces the lowest AIC testing out each number of K-values. Thanks for the help!

Thanks @RobHyndman. This was extremely helpful and it is making much more sense from your article. I attempted to manually calculate the first value with the sine function you provided. Am I not doing that part correctly? I included the formula in the question

I am fairly new to it but all I really know at this point is that it breaks down the data to extract the seasonality.

Thanks @whuber where should i ask that type of question?