# Inverse hyperbolic functions

This is an inverse hyperbolic functions calculator that accepts real and complex numbers.
input sqrt(2) for square root of 2 for example.

This tool calculates inverse hyperbolic functions inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cotangent for a given number.

## Inverse hyperbolic trigonometric functions in R (real numbers)

Function Abbreviation Domain Range
Inverse hyperbolic sine y = arsinh(x) all real numbers all real numbers
Inverse hyperbolic cosine y = arcosh(x) y >= 1 y >= 0
Inverse hyperbolic tangent y = artanh(x) -1 < y < 1 all real numbers
Inverse hyperbolic cotangent y = arcoth(x) y < -1 ou y > 1 all non-zero real

## Inverse hyperbolic sine

Also known as area hyperbolic sine, it is the inverse of the hyperbolic sine function and is defined by,

\text {arsinh} (x) = ln (x+sqrt (x^2+1))

arsinh(x) is defined for all real numbers x so the definition domain is RR.
The range (set of function values) is RR.

## Inverse hyperbolic cosine

Also known as area hyperbolic cosine, it is the inverse of the hyperbolic cosine function and is defined by,

\text {arcosh} (x) = ln (x+sqrt (x^2-1))

arcosh(x) is defined for real numbers x, x >= 1 so the definition domain is [1, +∞[.
The range (set of function values) is [0, +∞[.

## Inverse hyperbolic tangent

Also known as area hyperbolic tangent, it is the inverse of the hyperbolic tangent function and is defined by,

\text {artanh} (x) = frac {1} {2} *ln (frac {1+x} {1-x})

artanh(x) is defined for real numbers x between -1 and 1 so the definition domain is ]-1, 1[.
The range is the set of real numbers RR.

## Inverse hyperbolic cotangent

Also known as area hyperbolic cotangent, it is the inverse of the hyperbolic cotangent function and is defined by,

\text {arcoth} (x) = frac {1} {2} *ln (frac {x+1} {x-1})

arcoth(x) is defined for x < -1 ou x > 1 so the definition domain is ] -∞ , -1 [ U ] 1, +∞ [.
The range is the set of non-zero real numbers RR\ {0}.