MO, sorry I missed your post. I'm busy outside catching some rays at this time of year ... no time for the Internet.
Animation: Development of a Compound Angle on the Stick with Trigonometric ScalingAnimation: Compound Angle extracted from the stick and developedStill Life ... Development of a Compound AngleTrigonometric Analysis of the Compound AngleSummary of Compound Angle Formulas ... as of this post. There may be other formulas ...
Hope this helps. Now I'm going back into hibernation ...
EDIT: A caveat ... as noted in the diagrams, I generally use the term "miter" to mean the angle of saw travel measured on the stick. This is complementary to the angle on the saw gauge.
Some of the diagrrams and formulas on my web pages give the "miter angle" as the angle read on the saw. In other words, I have used the term "miter" both ways, so always check the diagrams.