Trigonometry plays a crucial role in mathematics, physics, engineering, and various other fields. In PHP, you have a powerful set of trigonometric functions at your disposal to perform complex calculations with ease. In this article, we will explore these PHP trigonometric functions, providing examples of how to use each one effectively. You can also reference the articles here and here that outline additional information on trig functions.

## The Fundamentals: Pi in PHP

In trigonometry, one fundamental constant is π (pi). PHP makes it simple to access the value of pi using the `pi()`

function, which returns the constant value 3.1415926535898.

echo pi(); // 3.1415926535898

## Converting Degrees to Radians with `deg2rad()`

When working with angles, you often need to convert between degrees and radians. PHP provides the `deg2rad()`

function for this purpose. It multiplies the degrees by π and divides the result by 180.

echo deg2rad(0); echo deg2rad(30); echo deg2rad(60); echo deg2rad(90); // Output: // 0.0 // 0.5235987755982988 // 1.0471975511965976 // 1.5707963267948966

## Converting Radians to Degrees with `rad2deg()`

Conversely, you can convert radians back to degrees using the `rad2deg()`

function. It multiplies the radians by 180 and divides by π.

echo rad2deg(0); echo rad2deg(pi()/6); echo rad2deg(pi()/3); echo rad2deg(pi()/2); // Output: // 0 // 30 // 60 // 90

## Calculating Sine with `sin()`

To calculate the sine of a number in radians, you can use the `sin()`

function. The input must be a float, and the return value will be a float ranging from -1 to 1.

echo sin(pi()/3); echo sin(0); echo sin(pi()/2); // Output: // 0.8660254037844386 // 0.0 // 1.0

## Calculating Cosine with `cos()`

For finding the cosine of a number in radians, PHP provides the `cos()`

function. It requires a float as input, and it returns a float between -1 and 1.

echo cos(pi()/3); echo cos(0); echo cos(pi()/2); // Output: // 0.5000000000000001 // 1.0 // 6.123233995736766e-17

## Determining Tangent with `tan()`

To calculate the tangent of a number, or the sine divided by the cosine of an angle in radians, use the `tan()`

function. The input must be a float, and the return value is a float ranging from negative infinity to infinity.

echo tan(pi()/3); echo tan(0); echo tan(pi()/2); // Output: // 1.7320508075688767 // 0.0 // 1.633123935319537e+16

## Finding Arcsine with `asin()`

The `asin()`

function is used to find the arcsine of a number. It requires a float between -1 and 1 as input and returns a float between -π/2 and π/2 radians.

echo asin(0.5); echo asin(0); echo asin(-0.75); // Output: // 0.5235987755982989 // 0.0 // -0.848062078981481

## Finding Arccosine with `acos()`

To determine the arccosine of a number, use the `acos()`

function. It requires a float between -1 and 1 as input and returns a float between 0 and π radians.

echo acos(0.5); echo acos(0); echo acos(-0.75); // Output: // 1.0471975511965979 // 1.5707963267948966 // 2.4188584057763776

## Calculating Arctangent with `atan()`

The `atan()`

function allows you to find the arctangent of a number. It requires a float as input and returns a float between -π/2 and π/2 radians.

echo atan(5); echo atan(0); echo atan(-3); // Output: // 1.373400766945016 // 0.0 // -1.2490457723982544

## Handling the Quotient of Two Numbers with `atan2()`

For finding the arctangent of the quotient of two numbers, represented as the coordinates of a point (x, y), you can use the `atan2()`

function. The inputs must be floats, and the return value is a float between -π and π radians.

echo atan2(5, 1); echo atan2(0, 0); echo atan2(-3, 7); // Output: // 1.373400766945016 // 0.0 // -0.40489178628508343

## Hyperbolic Functions

PHP also provides hyperbolic trigonometric functions:

`sinh()`

for hyperbolic sine`cosh()`

for hyperbolic cosine`tanh()`

for hyperbolic tangent`asinh()`

for hyperbolic arcsine`acosh()`

for hyperbolic arccosine`atanh()`

for hyperbolic arctangent

These functions operate in a similar manner to their standard trigonometric counterparts.

## Conclusion

Trigonometry is an essential branch of mathematics, and PHP’s extensive collection of trigonometric functions simplifies complex calculations in various applications. Whether you’re working with angles, coordinates, or hyperbolic values, PHP’s functions provide the tools you need to perform accurate and efficient calculations in your web applications and scripts. We hope this article has been helpful in demystifying PHP’s trigonometric functions and their applications.