C atan2() Function

Posted in C Tutorial

Updated on Jan 12, 2024

By Mari Selvan

👁️ 149 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In C programming, mathematical functions play a crucial role in various scientific and engineering applications.

The atan2() function is one such function provided by the C math library (<math.h>). It calculates the arctangent of the quotient of its arguments, providing a convenient way to compute the angle in radians between the positive x-axis of a plane and the point (x, y).

In this tutorial, we'll explore the usage and functionality of the atan2() function in C.

💡 Syntax

The syntax for the atan2() function is as follows:

Syntax

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double atan2(double y, double x);

y: The numerator (y-coordinate).
x: The denominator (x-coordinate).

The function returns the principal value of the arc tangent of y/x in the interval [−π,π] radians.

📄 Example

Let's dive into an example to illustrate how the atan2() function works.

atan2.c

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#include <stdio.h>
#include <math.h>

int main() {
  double y = 1.0;
  double x = 1.0;

  // Calculate the arctangent of y/x
  double result = atan2(y, x);

  // Convert radians to degrees for better readability
  double resultDegrees = result * (180.0 / M_PI);

  printf("atan2(%lf, %lf) = %lf radians\n", y, x, result);
  printf("atan2(%lf, %lf) = %lf degrees\n", y, x, resultDegrees);

  return 0;
}

💻 Output

Output

atan2(1.000000, 1.000000) = 0.785398 radians
atan2(1.000000, 1.000000) = 45.000000 degrees

🧠 How the Program Works

In this example, the atan2() function is used to calculate the arctangent of the ratio y/x where y=1.0 and x=1.0. The result is then printed in both radians and degrees.

↩️ Return Value

The atan2() function returns the arctangent of the specified ratio y/x in radians.

📚 Common Use Cases

The atan2() function is commonly used in graphics programming, robotics, and other fields where the need arises to calculate angles based on Cartesian coordinates. It is particularly useful for determining the orientation of a vector or the direction of one point relative to another.

📝 Notes

The atan2() function is preferred over atan(y/x) as it correctly handles the signs of both y and x, avoiding division by zero errors.
The result of atan2() is in the range of [−π,π] radians.

🎢 Optimization

The atan2() function is typically well-optimized in C libraries. No specific optimization is required on the user's part.

🎉 Conclusion

The atan2() function in C is a powerful tool for calculating angles based on Cartesian coordinates. It provides a convenient and reliable way to compute arctangents, especially in situations where the signs of both numerator and denominator are crucial.

Feel free to experiment with different values of y and x to explore the behavior of the atan2() function in various scenarios. Happy coding!