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Deriving the Bygrave equations
From: Bob Goethe
Date: 2018 Feb 6, 15:23 -0800

I can USE the Bygrave equations, but they are almost as much of a black box to me as is a GPS unit. I asked a young friend of mine who is a math major to walk me through how they were constructed, why they were true, and what all the derived intermediate values *mean*. He took the equations away and came back in a week to say that he specialized in calculus, and proving spherical trig equations was not his area.

I am only recently come to spherical trig, having become fascinated after I joined this group, rather than 50 years ago when I took trig in school. The level of my current comprehension is that I do understand how tan(θ) = LengthOpposite ÷ LengthAdjacent works. It makes sense to me, but taking that level of understanding to Bygrave is beyond me.

I would appreciate somebody walking me through the "why" and "how this works" of Bygrave's equations.

I know this is potentially a big-ask. Thank you so much for your time,

Bob

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