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Article 11 — Appendix A.12arsinh or arsh — archyperbolic sine functionCategory. Mathematics. Abstract. Archyperbolic sine: 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 sine is inverse of hyperbolic sine function. With the help of natural logarithm it can be represented as: arsinhx ≡ ln[x + √(x^{2} + 1)]2. GraphArchyperbolic sine is antisymmetric function defined everywhere on real axis. Its graph is depicted below — fig. 1. Fig. 1. Graph of the archyperbolic sine function y = arsinhx.Function codomain is entire real axis. 3. IdentitiesProperty of antisymmetry: arsinh−x = −arsinhxReciprocal argument: arsinh(1/x) = arcschxSum and difference: arsinhx + arsinhy = arsinh[x√(y^{2} + 1) + y√(x^{2} + 1)]arsinhx − arsinhy = arsinh[x√(y^{2} + 1) − y√(x^{2} + 1)] arsinhx + arcoshy = arsinh{xy + √[(x^{2} + 1)(y^{2} − 1)]} = arcosh[y√(x^{2} + 1) + x√(y^{2} − 1)] 4. SupportArchyperbolic sine function arsinh or arsh is supported in: Archyperbolic sine function of the complex argument sinh or sh is supported in:
5. How to useTo calculate archyperbolic sine of the number:
To calculate archyperbolic sine of the current result:
To calculate archyperbolic sine of the number x in memory:



