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

Syntax:

sin($angle_in_radians)

Parameters:

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

Return Value:

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

Important Note:

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

Example 1: Calculating Sine of an Angle in Radians

<?php
$angle_in_radians = pi() / 2;  // pi/2 radians (90 degrees)

// Calculate sine of the angle
$sine_value = sin($angle_in_radians);
echo $sine_value;
?>

Output:

1

In this example, $\sin(\pi/2)$ or $\sin(90^\circ)$ is 1.

Example 2: Calculating Sine of an Angle in Degrees

Since sin() expects radians, you need to use deg2rad() to convert an angle from degrees to radians.

<?php
$angle_in_degrees = 30;

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

// Calculate sine of the angle
$sine_value = sin($angle_in_radians);
echo $sine_value;
?>

Output:

0.5

In this case, $\sin(30^\circ)$ is 0.5.

Practical Usage:

• The sin() function is widely used in geometry, physics, engineering, and anywhere trigonometric calculations are required.
• It's particularly useful when dealing with periodic functions, oscillations, or when calculating the height or position in circular or wave-like motions.

Example 3: Using sin() for Simple Harmonic Motion

In physics, the position $y$ of an object in simple harmonic motion at time $t$ is given by the equation:

$$y = A \sin(\omega t)$$

Where:

• $A$ is the amplitude,
• $\omega$ is the angular frequency,
• $t$ is time.

<?php
$A = 10;              // Amplitude
$omega = pi();        // Angular frequency (radians per second)
$t = 2;               // Time in seconds

// Calculate position in simple harmonic motion
$y = $A * sin($omega * $t);
echo "Position at time t = 2s: " . $y;
?>

Output:

Position at time t = 2s: -10

Summary:

• sin() in PHP calculates the sine of an angle in radians.
• To use degrees, convert them to radians using deg2rad().
• It is frequently used in trigonometric, geometric, and physics-related calculations.