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, 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 $${\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}$$

There are several related functions corresponding to the versine:

Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation.

$${\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}$$

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: