The cos() function in PHP is used to calculate the cosine of a given angle, which is expected to be in radians. The cosine function is a fundamental trigonometric function that computes the ratio of the length of the adjacent side of a right-angled triangle to the length of the hypotenuse.

Syntax:

cos($angle_in_radians)

Parameters:

• $angle_in_radians: The angle in radians for which you want to calculate the cosine value.

Return Value:

• The function returns the cosine of the given angle as a float.

Important Note:

Since the cos() function expects the angle in radians, if your angle is in degrees, you need to convert it to radians using the deg2rad() function.

Example 1: Calculating Cosine of an Angle in Radians

<?php
$angle_in_radians = pi() / 3;  // pi/3 radians (60 degrees)

// Calculate cosine of the angle
$cosine_value = cos($angle_in_radians);
echo $cosine_value;
?>

Output:

0.5

In this example, $\cos(\pi/3)$ or $\cos(60^\circ)$ is 0.5.

Example 2: Calculating Cosine of an Angle in Degrees

To calculate the cosine of an angle given in degrees, convert it to radians using deg2rad().

<?php
$angle_in_degrees = 45;

// Convert degrees to radians
$angle_in_radians = deg2rad($angle_in_degrees);

// Calculate cosine of the angle
$cosine_value = cos($angle_in_radians);
echo $cosine_value;
?>

Output:

0.70710678118655

Here, $\cos(45^\circ)$ is approximately 0.7071.

Practical Usage:

• The cos() function is widely used in trigonometric calculations, particularly in geometry, physics, and engineering.
• It's useful for calculating the horizontal component of a vector, modeling periodic functions (e.g., waves, oscillations), or working with angles in various fields.

Example 3: Cosine in Physics (Projectile Motion)

In physics, the horizontal distance $x$ traveled by a projectile launched at an angle $\theta$ with an initial velocity $v$ can be calculated as:

$$x = v \cdot t \cdot \cos(\theta)$$

Where:

• $v$ is the initial velocity,
• $t$ is the time of flight,
• $\theta$ is the launch angle.

<?php
$v = 50;               // Initial velocity in meters per second
$t = 5;                // Time in seconds
$angle_in_degrees = 30; // Launch angle in degrees

// Convert degrees to radians
$angle_in_radians = deg2rad($angle_in_degrees);

// Calculate horizontal distance
$distance = $v * $t * cos($angle_in_radians);
echo "The horizontal distance is: " . $distance . " meters";
?>

Output:

The horizontal distance is: 216.50635094611 meters

Summary:

• cos() calculates the cosine of an angle in radians.
• If the angle is in degrees, use deg2rad() to convert it to radians before using cos().
• It is widely used in mathematical, physical, and engineering applications to compute angles, directions, or periodic functions.