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Article 11 — Appendix A.10arcoth or arcth — archyperbolic cotangent functionCategory. Mathematics. Abstract. Archyperbolic cotangent: definition, graph, properties and identities. References. This article is a part of scientific calculator LiL, scientific calculator LiX, scientific calculator LiLc and scientific calculator LiXc products. 1. DefinitionArchyperbolic cotangent is inverse of hyperbolic cotangent function. With the help of natural logarithm it can be represented as: arcothx ≡ ln[(1 + x) /(x − 1)] /22. GraphArchyperbolic cotangent is antisymmetric function defined everywhere on real axis, except the range [1, 1] — so, its domain is (−∞, −1)∪(1, +∞). Points x = ±1 are singular ones. Function graph is depicted below — fig. 1. Fig. 1. Graph of the archyperbolic cotangent function y = arcothx.Function codomain is entire real axis, except 0: (−∞, 0)∪(0, +∞). 3. IdentitiesProperty of antisymmetry: arcoth−x = −arcothxReciprocal argument: arcoth(1/x) = artanhxSum and difference: arcothx + arcothy = arcoth[(1 + xy) /(x + y)]arcothx − arcothy = arcoth[(1 − xy) /(x − y)] 4. SupportArchyperbolic contangent function arcoth or arcth is supported in: Archyperbolic contangent function of the complex argument arcoth or arcth is supported in:
5. How to useTo calculate archyperbolic cotangent of the number:
To calculate archyperbolic cotangent of the current result:
To calculate archyperbolic cotangent of the number x in memory:



