Welcome to the wonderful world of function decomposition. When learning about the work of Joseph Fourier it can be insightful to compare the structure with Laplace transforms, Taylor series, and learning a bit about functions as vectors.
Professor Brad Osgood, at Stanford University, introduces the subject from the point of view where the continuous integrals (the Fourier transform) becomes a limit of discrete infinite sums (the Fourier series). I like it, I think you will too.
Fourier Transforms at Stanford University
On Grant Sanderson's channel 3Blue1Brown he discusses how functions can be viewed as spanning vector spaces. In this context, the Fourier Transform can be seen as a change of basis.