The tanh is a Hyperbolic Tangent function. The **tanh()** function executes element-wise on arrays. The tanh function takes both real and complex data inputs. All angles are in radians.

In maths, the hyperbolic functions are analogs of the regular trigonometric functions but they are defined using a hyperbola rather than a circle.

The hyperbolic tangent of an angle *x* is the ratio of the **hyperbolic sine(sinh)** and **hyperbolic** **cosine(cosh)**.

In terms of the traditional tangent function with a complex argument, the identity is,

**tanh() Function in R**

The tanh() is an inbuilt mathematical R function that calculates the hyperbolic tangent of numeric data.

**Syntax**

```
tanh(x)
```

**Parameters**

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

**Example**

Let’s calculate the tanh value of 1.

`tanh(1)`

**Output**

`[1] 0.7615942`

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

`tanh(0)`

**Output**

`[1] 0`

**Plot the tanh() 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, tanh(dt), typ = "l", col = "red")
abline(v = 0, lty = 6, col = "blue")
```

**Output**

**Applying tanh() function to a Vector**

To create a Vector in R, use the c() function. Then pass that vector to the tanh() function.

```
rv <- c(-1, 0.5, 0, 0.5, 1)
tanh(rv)
```

**Output**

`[1] -0.7615942 0.4621172 0.0000000 0.4621172 0.7615942`

**Passing a pi to the tanh() function**

The **pi **is an inbuilt constant in R programming, and its value is **3.141593**.

Let’s find the pi constant’s **tanh()** value.

`tanh(pi)`

**Output**

```
[1] 0.9962721
```

Let’s see another example of pi.

`tanh(pi / 4)`

**Output**

`[1] 0.6557942`

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