I've thought that I needed some such when I last taught trigonometry. Sure, it's a graphical introduction to the applied math of Fourier series. The OP starte

I've thought that I needed some such when I last taught trigonometry. Sure, it's a graphical introduction to the applied math of Fourier series. The OP started saying that the horizontal axis was time but later discussed 180 degrees without connecting degrees with time. Why the harmonic frequencies are distinct positive whole number multiples of the fundamental frequency? Because the sine waves at those frequencies form an orthogonal coordinate system with all the advantages of such a system in 2 and 3 dimensions we know well. Similarly for linear algebra with positive whole number dimensions. So, right, the periodic waves are in a vector space of countably infinite dimensions. Usually in practice we can get good approximations by considering only the first dozen or two harmonics. The waves travel according to the wave equation. It would be good to connect with that. The lecture might have discussed the effect of tone controls and linear systems and linear filtering more generally.