[ten_fingers]

> Those all fall under the umbrella I gave.

Yes, all or nearly all! That the trig functions are the source of the most important orthogonal basis in Hilbert space theory need not be good to know just for physics or signal processing!

Let's see: Also I mentioned characteristic functions and Bochner's theorem which are core probability and not just physics or signal processing. Characterization of time invariant linear systems might be in mechanical engineering and might be tried even in economics! Seismic data analysis via the fast Fourier transform is, yes, in signal processing but is also mostly regarded as geology or just looking for oil or anything 'down there'.

I tried, as you can see, I really tried, to show how trig was for more than just your father's topics in physics and signal processing. I tried!