Trigonometry and Its History II - Obtuse Angles and the Curious History of the Cosine Rule

I talk about how I like to develop trigonometry, give some of my favourite proofs, and explore the history. The history of the sine rule is simple - it' over 1300 years old. The cosine rule took much longer and was only fully formed some 200 years ago. I explore why that is.

[@KipIngram]

That's really very neat, how you can use the half angle formula to carry the exact values all the way down as finely as you like. And then as soon as you get to a fine enough resolution to ensure the accuracy you want, you can use finite differences to interpolate in between that last round of exact values, to get your table entries on whatever spacing you want.
I may have to write a Python program to do this. Maybe generate a nice LaTeX table set. 🙂 Or heck, even just a plain text set.