PHP acosh() Function

The acosh() function returns the inverse hyperbolic cosine of a given number. The inverse hyperbolic cosine is defined mathematically as:

acosh(x) = log(x + sqrt(x² - 1))

This function accepts values greater than or equal to 1 and returns a float value representing the hyperbolic angle in radians.

Syntax

acosh(float $arg): float

Parameters

Return Value

Returns the inverse hyperbolic cosine of arg as a float, or NAN if arg is less than 1.

Example 1: Basic Usage

Calculate acosh() for different values and verify with the mathematical formula ?

<?php
    $arg = M_PI_2;  // ?/2 ? 1.5708
    $val = acosh($arg);
    $formula_result = log($arg + sqrt(pow($arg, 2) - 1));
    
    echo "acosh(" . $arg . ") = " . $val . "<br>";
    echo "Formula result = " . $formula_result . "<br>";
    echo "Match: " . ($val == $formula_result ? "Yes" : "No");
?>

acosh(1.5707963267949) = 1.0232274785476
Formula result = 1.0232274785476
Match: Yes

Example 2: Different Values

Testing acosh() with various input values ?

<?php
    $values = [1, 2, M_PI, 5.5];
    
    foreach ($values as $val) {
        $result = acosh($val);
        echo "acosh($val) = " . round($result, 6) . "<br>";
    }
?>

acosh(1) = 0
acosh(2) = 1.316958
acosh(3.1415926535898) = 1.811526
acosh(5.5) = 2.40441

Example 3: Error Handling

Demonstrating behavior with invalid input values ?

<?php
    $invalid_values = [0.5, 0, -1];
    
    foreach ($invalid_values as $val) {
        $result = acosh($val);
        if (is_nan($result)) {
            echo "acosh($val) = NAN (invalid input)<br>";
        } else {
            echo "acosh($val) = $result<br>";
        }
    }
?>

acosh(0.5) = NAN (invalid input)
acosh(0) = NAN (invalid input)
acosh(-1) = NAN (invalid input)

Conclusion

The acosh() function calculates inverse hyperbolic cosine for values ? 1, returning NAN for invalid inputs. It's useful in mathematical calculations involving hyperbolic functions and geometric computations.