atanh() Function in R with Example

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).

R tanh(T x)

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.




x: It is a numeric value, array, or vector.


Let’s calculate the atanh value of 1.



[1] Inf

If you pass the 0 to the atanh() function, it will return 0.



[1] 0

Calculate atanh() of complex number

Define a complex value and pass that value to the atanh() function.

d <- 5 + 1i


[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")


atanh() Function in R with Example

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)


[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.



[1] NaN
Warning message:
In atanh(pi) : NaNs produced

Let’s see another example of pi.

atanh(pi / 4)


[1] 1.059306

That is it for atanh() function in R programming.

See also

R acos()

R asin()

R atan()

R tan()

R sin()

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