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Frank wrote

Of course, if you have a calculator, there's no reason to use the Bygrave equations except to confirm your paper calculations. But if you're checking paper calculations, then go ahead and run them up on your calculator without worries.

Frank maybe you can clarify something for me. A while ago I was browsing and found a forum in which the members were discussing how to calculate the distance between two points. They were excited because they had discivered haversines and believed that the function gave better accuracy than the cosine. I think that they were confused. IIRC  the haversine was introduced because you cannot take the log of a negative number. The only reason you would use logs is if you were doing the calculation manually. The forum was clearly about electronic calculations so I concluded that their use of the haversine was completely uneccessary.

As an aside if they were talking about short distances than Pythagoras would have sufficed.