Template:Arcosh/doc

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The {{arcosh}} (inverse) hyperbolic function template returns the inverse hyperbolic cosine of $\scriptstyle x\,$, where $\scriptstyle x,\,x\,\geq \,1,\,$ is a real number.

Usage

{{arcosh|a real number greater than or equal to 1}}

Valid input

A real number greater than or equal to 1 as argument.

Examples

Examples with valid input

Code	Result
{{arcosh|1}}	0
{{arcosh|2}}	1.3169578969248
{{arcosh|5}}	2.2924316695612
{{arcosh|{{cosh|-1}}}}	0.99999999999996
{{arcosh|{{cosh|-0.5}}}}	0.50000000000004
{{arcosh|{{cosh|0}}}}	0
{{arcosh|{{cosh|0.5}}}}	0.50000000000004
{{arcosh|{{cosh|1}}}}	0.99999999999996

Examples with invalid input (returns an error message)

Code	Result
{{arcosh|i}}
{{arcosh|-1}}
{{arcosh|-0.5}}
{{arcosh|0}}
{{arcosh|0.5}}

Code

{{ifnum| {{{1|not a number}}}
| {{#ifexpr: ({{{1}}}) >= 1
  | {{#expr: ln ( ({{{1}}}) + ( ({{{1}}})^2 - 1 )^(1/2) ) }}
  | {{error| Arcosh error: Argument must be a real number greater than or equal to 1}}
  }}
| {{error| Arcosh error: Argument must be a real number greater than or equal to 1}}
}}

See also

• Hyperbolic functions
• Inverse hyperbolic functions

• {{sinh}}
• {{cosh}}
• {{tanh}}

• {{csch}}
• {{sech}}
• {{coth}}

• {{arsinh}} (see also {{qlog}})
• {{arcosh}}
• {{artanh}}

• {{arcsch}}
• {{arsech}}
• {{arcoth}}