Property	Value
Hex Value	`$CD`
Categories	Catalog > T
Localizations	FR: `Argth(`

`tanh⁻¹(`

Overview

Returns the hyperbolic arctangent of a real number, expression, or list.

Availability: Token available everywhere.

Syntax

tanh⁻¹(value)

Arguments

Name	Type	Optional
⁻¹	real\|expression\|real[]
value	real\|expression\|real[]

Location

2nd, catalog, tanh

Description

The tanhֿ¹( command calculates the inverse hyperbolic tangent of a value. tanhֿ¹(x) is the number y such that x = tanh(y).

tanhֿ¹(x), although it can be defined for all real and complex numbers, is real-valued only for x in the open interval (-1,1). Since Z80 calculators have their hyperbolic functions and inverses restricted to real values, ERR:DOMAIN is thrown when x is outside the interval (-1,1).

The tanhֿ¹( command also works for lists.

tanhֿ¹(0)
    0
tanhֿ¹({-.5,.5})
    {-.5493061443 .5493061443}

Error Conditions

ERR:DOMAIN when taking the inverse tanh of a number not between -1 and 1.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

History

Calculator	OS Version	Description
TI-82	1.0	`tanh⁻¹` added
TI-83	0.01013	Renamed `tanh⁻¹` to `tanh⁻¹(`

Authors: Adrien Bertrand

tanh⁻¹(