# Perl Math - acosh() Function

The Perl Math acosh() function returns inverse hyperbolic cosine of a value. The inverse hyperbolic cosine of x is defined as:

### Syntax

```acosh(x)
```

### Parameters

 `x` Specify the value.

### Return Value

Returns the inverse hyperbolic cosine of a value.

### Example:

In the example below, acosh() function is used to find out the inverse hyperbolic cosine of a value.

```use Math::Trig;

print("acosh(1) = ".acosh(1)."\n");
print("acosh(2) = ".acosh(2)."\n");
print("acosh(3) = ".acosh(3)."\n");
print("acosh(4) = ".acosh(4)."\n");
print("acosh(Inf) = ".acosh(Inf)."\n");
```

The output of the above code will be:

```acosh(1) = 0
acosh(2) = 1.31695789692482
acosh(3) = 1.76274717403909
acosh(4) = 2.06343706889556
acosh(Inf) = Inf
```

This function can also be used to calculate complex inverse hyperbolic cosine of a complex number z. It is a function on complex plane, and has one branch cut, extending left from 1 along the real axis to -∞, continuous from above.

Mathematically, it can be expressed as:

### Example:

In the example below, acosh() function is used to find out the complex inverse hyperbolic cosine of a given complex number.

```use Math::Complex;

\$z1 = 2 + 2*i;
\$z2 = 2;
\$z3 = 2*i;
print("acosh(\$z1) = ".acosh(\$z1)."\n");
print("acosh(\$z2) = ".acosh(\$z2)."\n");
print("acosh(\$z3) = ".acosh(\$z3)."\n");
```

The output of the above code will be:

```acosh(2+2i) = 1.73432452148797+0.816547182096851i
acosh(2) = 1.31695789692482
acosh(2i) = 1.44363547517881+1.5707963267949i
```

❮ Perl Math Functions

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