Category. Mathematics.
Abstract. Arc-hyperbolic cosine: definition, plot, properties and identities.
Reference. This article is a part of Librow scientific formula calculator project.
Arc-hyperbolic cosine is inverse of hyperbolic cosine function. With the help of natural logarithm it can be represented as:
arcoshx ≡ ln[x + √(x2 − 1)]Arc-hyperbolic cosine is monotone function defined in the range [1, +∞). Its plot is depicted below — fig. 1.
[画像:Fig. 1. Plot of the arc-hyperbolic cosine function y = arcosh x.] Fig. 1. Plot of the arc-hyperbolic cosine function y = arcoshx.Function codomain is non-negative part of real axis: [0, +∞).
Reciprocal argument:
arcosh(1/x) = arsechxSum and difference:
arcoshx + arcoshy = arcosh{xy + √[(x2 − 1)(y2 − 1)]}Arc-hyperbolic cosine function arcosh or arch of the real argument is supported by free version of the Librow calculator.
Arc-hyperbolic cosine function arcosh or arch of the complex argument is supported by professional version of the Librow calculator.
To calculate arc-hyperbolic cosine of the number:
arcosh(2);To calculate arc-hyperbolic cosine of the current result:
arcosh(rslt);To calculate arc-hyperbolic cosine of the number x in memory:
arcosh(mem[x]);