The **arccosine** of x is defined as the inverse cosine **function** of x when -1≤x≤1.

When the cosine of y is equal to x:

`cos y = x`

Then the **arccosine** of x is equal to the inverse cosine **function** of x, which is equal to y:

`arccos x = cos^-1 x = y`

Here cos^{-1} x means the inverse cosine and does not mean cosine to the power of -1.

**acosh() Function in R**

To calculate the hyperbolic arccosine in R, use the acosh() function. The inverse hyperbolic cosine function is defined by x == cosh(y). The acosh(x) returns the inverse hyperbolic cosine of the elements of x when x is a REAL scalar, vector, matrix, or array. The result has the same shape as x.

**Syntax**

`acosh(x)`

**Parameters**

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

**Example**

Let’s calculate the acosh value of 1.

`acosh(1)`

**Output**

`[1] 0`

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

`acosh(0)`

**Output**

`[1] 0`

**Calculate acosh() of complex number**

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

```
dt <- 8 + 9i
acosh(dt)
```

**Output**

`[1] 3.181721+0.845865i`

**Plot the acosh() 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 = 0.01)
plot(dt, acosh(dt), type = "l", col = "red")
```

**Output**

```
Warning message:
In acosh(dt) : NaNs produced
```

The function returns the NaN value that is why it can’t draw a graph based on that value.

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

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

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

**Output**

```
[1] NaN NaN NaN NaN 0
Warning message:
In acosh(rv) : NaNs produced
```

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

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

Let’s find the pi constant’s acosh() value.

`acosh(pi)`

**Output**

`[1] 1.811526`

Let’s see another example of pi.

`acosh(pi / 4)`

**Output**

```
[1] NaN
Warning message:
In acosh(pi/4) : NaNs produced
```

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