Versine

Part of speech: noun

Definitions

1. A mathematical function that represents the difference between one and the cosine of an angle
2. The value calculated as 1 minus the cosine of a specific angle, often used in trigonometry
3. A trigonometric term denoting the complement of the cosine, relevant in various mathematical applications

Etymology: Versine is a trigonometric function, and its name is a compound that records a change in how mathematicians thought about angles. It is formed from Latin "versus", the past participle of "vertere" ("to turn"), combined with "sine". The "versed sine" was the Latin-derived name for the quantity 1 minus the cosine, and the shortened form "versine" came into use later. The sine itself was originally a half-chord in a circle: Indian and Arabic astronomers measured a chord and its half-length, and the translators who carried these ideas into Latin took the Arabic term "jiba" and rendered it as "sinus", meaning "bay" or "fold", which became "sine". The versed sine was the distance from the chord's midpoint to the arc, the "turned" part of the sine, which is how the name arose. Versines were once practical tools for navigators and surveyors. Because the function is never negative and stays small for small angles, it simplified the calculation of spherical triangles and was tabulated in logarithmic tables. Its use declined as calculators made it unnecessary, and the term survives mainly in historical mathematics texts.