The atanh() function works both for real and complex numbers. For real number, -1 < x < 1. For complex number, the range is -Inf < x < -1 and 1 < x < Inf.
Hyperbolic Trigonometric Functions
The hyperbolic cosine of x (in radians).
The hyperbolic sine of x (in radians).
The hyperbolic tangent of x (in radians).
It is an inverse hyperbolic cosine (in radians).
It is an inverse hyperbolic cosine (in radians).
R atanh(T x)
It is an inverse hyperbolic tangent (in radians) of x.
atanh in R
The atanh() is a built-in R function that returns the inverse hyperbolic tangent. It accepts the vector, scalar, matrix, or array and returns the hyperbolic tangent of the provided object.
To calculate the hyperbolic arctangent in R, use the atanh() function. For example, the atanh(x) returns the inverse hyperbolic tangent of the elements of x when x is a REAL scalar, vector, matrix, or array.
The result has the same shape as x.
Syntax
atanh(x)
Parameters
x: It is a numeric value, array, or vector.
Example
Let’s calculate the atanh value of 1.
atanh(1)
Output
[1] Inf
If you pass the 0 to the atanh() function, it will return 0.
atanh(0)
Output
[1] 0
Calculating atanh() of complex number
Define a complex value and pass that value to the atanh() function.
d <- 5 + 1i
atanh(d)
Output
[1] 0.194426+1.530881i
Plot the atanh() function to a graph
We can use the seq() function to create a series of values and pass that to the plot() function, which will create a line chart.
dt <- seq(-1, 1, by = 0.05)
plot(dt, atanh(dt), typ = "l", col = "red")
abline(v = 0, lty = 6, col = "blue")
Output
Applying atanh() function to a Vector
To create a Vector in R, use the c() function. Then pass that vector to the atanh() function.
rv <- c(-1, 0.5, 0, 0.5, 1)
atanh(rv)
Output
[1] -Inf 0.5493061 0.0000000 0.5493061 Inf
Passing a pi to the atanh() function
The pi is an inbuilt constant in R programming, and its value is 3.141593.
Let’s find the pi constant’s atanh() value.
atanh(pi)
Output
[1] NaN
Warning message:
In atanh(pi) : NaNs produced
Let’s see another example of pi.
atanh(pi / 4)
Output
[1] 1.059306
That is it for the atanh() function overview.
See also

Krunal Lathiya is an Information Technology Engineer by education and web developer by profession. He has worked with many back-end platforms, including Node.js, PHP, and Python. In addition, Krunal has excellent knowledge of Data Science and Machine Learning, and he is an expert in R Language. Krunal has written many programming blogs, which showcases his vast expertise in this field.