Well, if you understood the origins, you could picture the DG as a unit circle and calculate your sin and cos from there. Close enough for a rough inflight calculation.
I do understand the unit circle, it’s what I was alluding to and I personally picture the unit circle with important points measured in radians not degrees since pretty much everything I work with with trig functions uses radians not degrees. It sort of ties into the Spock picture above. If we were to meet an alien industrialized civilization, they probably wouldn’t have a 360 degree measure because that’s completely arbitrary. (The French for instance came up with a 400 gradians system for example). However, they would have the concept of radians since that’s based fundamentally on the geometry of a circle. They would also have the notion of pi (or tau) and a representation of e.
The point I was trying to make is that it’s not necessary to be so exact to actually use trig functions. Just putting a spot on a circle and rotating (like on the whiz wheel) will give you an intuitive notion of how the crosswind component changes as the wind moves relative to your flight path, and with the winds aloft functions being very inexact, a guesstimate from this intuitive knowledge is good enough to give you a heading which will get you close enough to the next way point that you can then re-estimate and correct.
