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
R cosh(T x)
The hyperbolic cosine of x (in radians).
R sinh(T x)
The hyperbolic sine of x (in radians).
The hyperbolic tangent of x (in radians).
R acosh(T x)
It is an inverse hyperbolic cosine (in radians).
R asinh(T x)
It is an inverse hyperbolic cosine (in radians).
R atanh(T x)
It is an inverse hyperbolic tangent (in radians) of x.
atanh() Function in R
To calculate the hyperbolic arctangent in R, use the atanh() function. 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
Calculate 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 atanh() function in R programming.