# atan2() function in C

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##
**Introduction to atan2() Function in C
**

The **atan2() function in C** is used to **compute** the** arc tangent **of the two variables **y** and** x**.

Unlike the basic **atan() function**, which only takes a** single argument**, **atan2(y, x) **takes two arguments and returns the angle in radians between the** positive x-axis** and the **point (x, y)**.

This function is particularly useful for converting **Cartesian coordinates** to** polar coordinates**.

**Syntax atan2() Function in C:
**

#include<math.h>double atan2(double y, double x);

**Example:**

**Program 1: Basic Usage of atan2()
**

// program to demonstrates the basic use of theatan2() functionby calculating the angle for givenyandx coordinates. #include <stdio.h>#include <math.h> int main() { double y = 5.0; double x = 3.0; double angle = atan2(y, x); printf("The angle between the positive x-axis and the point (%.2f, %.2f) is %.2f radians\n", x, y, angle); return 0; }

**Output:
**

The angle between the positive x-axis and the point (3.00, 5.00) is 1.03 radians

**Program 2: Converting Cartesian Coordinates to Polar Coordinates
**

// program to converts Cartesian coordinates (x, y) to polar coordinates (r, θ) using atan2() to compute the angle θ. #include <stdio.h>#include <math.h> int main() { double x = 3.0; double y = 4.0; double r = sqrt(x*x + y*y); // Calculating the radius double theta = atan2(y, x); // Calculating the angle printf("Cartesian coordinates (%.2f, %.2f) -> Polar coordinates (r: %.2f, θ: %.2f radians)\n", x, y, r, theta); return 0; }

**Output:
**

Cartesian coordinates (3.00, 4.00) -> Polar coordinates (r: 5.00, θ: 0.93 radians)

##
**Uses of atan2()
**

**Converting Cartesian to Polar Coordinates: **atan2() is widely used to **convert (x, y)** Cartesian coordinates to **polar coordinates**, providing a more intuitive angle measurement.

**Robotics and Navigation:** In robotics and navigation systems, **atan2() **helps determine direction and orientation by calculating angles between different points.

**Computer Graphics: **In graphics programming, **atan2() **can be used to** rotate objects**, calculate angles for transformations, and determine **orientations of graphical**
**entities**.

**Signal Processing:** For phase angle calculations in **complex signal processing**, **atan2() **is essential for accurate results.

**Physics Simulations: **Simulations involving** projectile motion**,** circular motion**, or any** scenario **requiring angle calculation between vectors rely on **atan2() **for precision.

By understanding and using the** atan2() function**, programmers can accurately handle a variety of tasks involving **angle calculations **and** coordinate transformations**.

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