Exsecant
The external secant function (abbreviated exsecant, symbolized exsec) is a trigonometric function defined in terms of the secant function: exsec θ = sec θ − 1 = 1 cos θ − 1. {\displaystyle \operatorname {exsec} \theta =\sec \theta -1={\frac {1}{\cos \theta }}-1.} It was introduced in 1855 by American civil engineer Charles Haslett, who used it in conjunction with the existing versine function, vers θ = 1 − cos θ , {\displaystyle \operatorname {vers} \theta =1-\cos \theta ,} for designing and measuring circular sections of railroad track.