when Charles Haslett published the first known table of exsecants. Variations such as ex secant and exsec were in use in 1880, and exsecant was used since 1894 the least. The terms coexsecant and coexsec can be found used as early as 1880 as well followed by excosecant since 1909. The function was also utilized by Albert Einstein to describe the kinetic energy of fermions. Mathematical identities Derivatives Integrals Inverse functions The inverse functions arcexsecant (arcexsec, aexsec, aexs, exsec−1) and arcexcosecant (arcexcosec, arcexcsc, aexcsc, aexc, arccoexsecant, arccoexsec, excsc−1) exist as well: (for y ≤ −2 or y ≥ 0) Other properties Derived from the unit circle: The exsecant function is related to the tangent function by In analogy, the excosecant function is related to the cotangent function by The exsecant function is related to the sine function by In analogy, the excosecant function is related to the cosine function by The exsecant and excosecant functions can be extended into the complex plane. See also References Trigonometric functions