How to calculate direction angle using deg2rad and tan?

1. Definition and calculation background of direction angle

Direction angles usually represent the angle at which a point rotates clockwise relative to the reference direction (such as north). In a planar coordinate system, we often need to calculate the direction angle between two points based on the coordinates of them.

Suppose there are two points (x1, y1) and (x2, y2) , we want to calculate the direction angle pointing from point 1 to point 2.

2. Basic ideas for calculating direction angles using deg2rad and tan functions

In mathematics, the direction angle can be calculated by the following formula:

here, $\Delta x = x_2 - x_1$ , $\Delta y = y_2 - y_1$ .

In PHP, tan() is a tangent function, atan() is an arctangent function; deg2rad() is used to convert angles to radians, because the parameters accepted by the trigonometric function are radians.

When calculating the direction angle, we usually need to get the arctangent value (radians) first and then convert it to the angle.

3. PHP code examples

 <?php
// Start and end coordinates
$x1 = 10;
$y1 = 15;
$x2 = 20;
$y2 = 25;

// Calculate the coordinate difference
$dx = $x2 - $x1;
$dy = $y2 - $y1;

// Calculate the radian value of the direction angle，Notice atan2 Can distinguish quadrants
$angleRad = atan2($dy, $dx);

// Convert radians to angles
$angleDeg = rad2deg($angleRad);

// Direction angles usually need to be converted to 0-360 Between degrees
if ($angleDeg < 0) {
    $angleDeg += 360;
}

echo "The direction angle is：".$angleDeg." Degree";
?>

The above code demonstrates how to calculate the direction angle using atan2() , atan2() is a calculation $\arctan(\frac{y}{x})$ is more accurate function that can automatically handle angles in different quadrants to avoid errors.

4. Why not just tan and deg2rad?

tan() is a function used to calculate tangent values, not angles. What is required to calculate the direction angle is the arctangent function atan() or the more perfect atan2() . deg2rad() is a helper function used to convert degrees into radians. It is mainly used to input angle radians to facilitate calling trigonometric functions.

If you use tan() to directly calculate the angle, the process is wrong. You need to calculate the angle (radian) first using coordinates, and then convert it to angle.

5. Summary

• When calculating the direction angle, the focus is to use atan2() to obtain the correct radian value;

• deg2rad() is used to convert angles into radians, suitable for calling trigonometric functions when you already have angle values;

• The direction angle should be standardized in the range of 0-360 degrees;

• The tan() function itself is only suitable for finding tangent values ​​and is not used to inversely calculate angles.

After mastering the above knowledge points, you can use PHP to accurately calculate the direction angle between the two points.