The atan() function in PHP is used to calculate the arctangent (inverse tangent) of a given value. The arctangent function returns the angle (in radians) whose tangent is the specified value. This function is particularly useful when you have a tangent value and need to determine the corresponding angle.

Syntax:

atan($value)

Parameters:

• $value: A float representing the tangent value for which you want to calculate the arctangent.

Return Value:

• The function returns the arctangent of the value in radians as a float.

Example 1: Calculating Arctangent of a Value

<?php
$value = 1;

// Calculate arctangent
$arctangent_value = atan($value);
echo $arctangent_value;
?>

Output:

0.78539816339745

In this example, the arctangent of 1 is approximately $\frac{\pi}{4}$ radians (or 45 degrees).

Example 2: Converting Arctangent to Degrees

To convert the result from radians to degrees, you can use the rad2deg() function.

<?php
$value = 1;

// Calculate arctangent in radians
$arctangent_value = atan($value);

// Convert radians to degrees
$arctangent_degrees = rad2deg($arctangent_value);
echo "Arctangent in degrees: " . $arctangent_degrees;
?>

Output:

Arctangent in degrees: 45

Example 3: Handling Negative Values

The atan() function can also handle negative values, returning angles in the range of $-\frac{\pi}{2}$ to $\frac{\pi}{2}$.

<?php
$value = -1;

// Calculate arctangent
$arctangent_value = atan($value);
echo $arctangent_value;
?>

Output:

-0.78539816339745

In this case, the arctangent of -1 is approximately $-\frac{\pi}{4}$ radians (or -45 degrees).

Practical Usage:

• The atan() function is commonly used in trigonometry and geometry when determining angles based on tangent values.
• It is particularly useful in applications involving physics, engineering, and computer graphics where you might need to compute angles based on the ratios of sides.

Example 4: Using atan2() for Two-Dimensional Angles

In many cases, you might want to calculate the angle based on both the x and y coordinates of a point. For this purpose, PHP provides the atan2() function, which computes the arctangent of the quotient of its arguments, providing a full range of angles.

<?php
$y = 1;  // Opposite side
$x = 1;  // Adjacent side

// Calculate angle using atan2
$angle = atan2($y, $x);
echo "Angle in radians: " . $angle;
echo "Angle in degrees: " . rad2deg($angle);
?>

Output:

Angle in radians: 0.78539816339745
Angle in degrees: 45

Summary:

• atan() calculates the arctangent (inverse tangent) of a value, returning the angle in radians.
• It can handle both positive and negative values, returning angles in the range of $-\frac{\pi}{2}$ to $\frac{\pi}{2}$.
• To convert from radians to degrees, you can use rad2deg().
• For two-dimensional angles, consider using atan2(), which provides more robust angle calculations.