What is the atanh() Function in R

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The atanh() function in R is “used to calculate the inverse hyperbolic tangent of a number”. For real numbers, -1 < x < 1. For complex numbers, the range is -Inf < x < -1 and 1 < x < Inf.

Syntax

atanh(x)

Parameters

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

Example 1: How to use the atanh() function

atanh(1)

Output

[1] Inf

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

atanh(0)

Output

[1] 0

Example 2: Calculating atanh() of a complex number

d <- 5 + 1i
atanh(d)

Output

[1] 0.194426+1.530881i

Example 3: Using atanh() function to a Vector

rv <- c(-1, 0.5, 0, 0.5, 1)
atanh(rv)

Output

[1] -Inf 0.5493061 0.0000000 0.5493061 Inf

Example 4: Passing a pi to the atanh() function

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

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, creating 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

atanh() Function in R with Example

Other 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.

That is it.

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