...they don't let you solve any problem that you couldn't before
But they did have a purpose, years ago. Before pocket calculators, when people used slide rules and log tables, a table of haversines helped avoid nasty loss-of-precision errors near the roots of a function.
To emphasize your response, the article goes into depth on this exact point:
> I must admit I was a bit disappointed when I looked these up. They’re all just simple combinations of dear old sine and cosine. Why did they even get names?! ...
> The secret trig functions, like logarithms, made computations easier. Versine and haversine were used the most often. Near the angle θ=0, cos(θ) is very close to 1. If you were doing a computation that had 1-cos(θ) in it, your computation might be ruined if your cosine table didn’t have enough significant figures.
But they did have a purpose, years ago. Before pocket calculators, when people used slide rules and log tables, a table of haversines helped avoid nasty loss-of-precision errors near the roots of a function.