Sinus verse

The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Aryabhatia, Section I) trigonometric tables. The versine of an angle is 1 minus its cosine. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation. The versine or versed sine is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin, sinver, vers, ver or siv. In Latin, it is known as the sinus versus (flipped sine), versinus, versus, or sagitta (arrow). Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to There are several related functions corresponding to the versine: The versed cosine, or vercosine, abbreviated vercosin, vercos, or vcs. The coversed sine or coversine (in Latin, cosinus versus or coversinus), abbreviated coversin, covers, cosiv, or cvs The coversed cosine or covercosine, abbreviated covercosin, covercos, or cvc In full analogy to the above-mentioned four functions another set of four "half-value" functions exists as well: The haversed sine or haversine (Latin semiversus), abbreviated haversin, semiversin, semiversinus, havers, hav, hvs, sem, or hv, most famous from the haversine formula used historically in navigation The haversed cosine or havercosine, abbreviated havercosin, havercos, hac or hvc The hacoversed sine, hacoversine, or cohaversine, abbreviated hacoversin, semicoversin, hacovers, hacov or hcv The hacoversed cosine, hacovercosine, or cohavercosine, abbreviated hacovercosin, hacovercos or hcc The ordinary sine function (see note on etymology) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine (sinus versus). The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle: For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ) is the distance AC (half of the chord).