Definition
The haversine of an angle equals half of one minus its cosine, a function chosen because it is always positive, which removes sign ambiguity, and because it behaves well for small angles. Traditional reduction used log haversines with Norie's or Burton's tables, adding logarithms rather than multiplying. The method remains a valid backup and appears in some examination syllabuses, but it demands careful bookkeeping and is slower than either modern tables or a calculator.
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