In a nutshell, the sin() and cos() terms are periodic curves, and the weighting of the various coefficients is what allows proper regression fits. Let’s take a closer look at the formula, and try to make sense of it.

As t (weeks) increases to 52, goes from 0 to 1 (, , , , …, ) Once it goes past 52, it just cycles around again. Recall radians = 360 degrees. Since is multiplied by , it is multiplying 360 by some number. So, it seems the sin() and cos() terms simply use t weeks to scale across multiples of 360 degrees .

For example, as t goes from 0 to 52, goes from 0 to 1, goes from 0 and 360. (and then it repeats since sin repeats in multiples of and therefore goes from sin(0) to sin(360) which is a full periodic cycle of this function. Note the same logic applies to the cos() term in the formula.