The hyperbolic functions are analogs of the circular function or the trigonometric functions. The hyperbolic function occurs in the solutions of linear differential equations, calculation of distance and angles in the hyperbolic geometry, Laplace’s equations in the cartesian coordinates.

**Equation of sinh() function**

The equation of the sinh() function is the following.

The hyperbolic functions are defined within the algebraic expressions, including the exponential function (e^x) and its inverse exponential functions (e^-x), where e is the Euler’s constant.

**sinh() Function in R**

To calculate the hyperbolic sine value of the numeric value in R, use the **sinh()** **function**. The **sinh()** is an inbuilt mathematical R function that calculates the hyperbolic sine of the given value.

**Syntax**

`sinh(x)`

**Parameters**

**x:** It is a numeric value.

**Example**

```
sinh(0)
sinh(1)
```

**Output**

```
[1] 0
[1] 1.175201
```

**Calculate sinh() of complex number**

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

```
d <- 5 + 1i
sinh(d)
```

**Output**

`[1] 40.09217+62.44552i`

**Plot the sinh() function to a graph**

We will use the seq() function to create a series of values and pass that to the plot() function, which will create a line chart using the sinh() function.

```
dt <- seq(-1, 1, by = 0.05)
plot(dt, sinh(dt), typ = "l", col = "red")
abline(v = 0, lty = 6, col = "blue")
```

**Output**

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

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

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

**Output**

`[1] -1.1752012 0.5210953 0.0000000 0.5210953 1.1752012`

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

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

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

`sinh(pi)`

**Output**

`[1] 11.54874`

Let’s see another example of **pi**.

`sinh(pi / 4)`

**Output**

`[1] 0.868671`

That is it for **sinh()** function in R programming.