What is the key difference between atan and atan2 functions in C ?

The Difference Between atan and atan2 in C

In trigonometry, the arctangent function (atan) calculates the angle whose tangent is a given value. However, atan has a limitation in that it only returns angles from the first or fourth quadrant (-π/2 <= atan() <= π/2), regardless of the input.

To overcome this limitation, C provides the atan2 function. Unlike atan, which only takes one argument (the tangent), atan2 takes two arguments: the sine and cosine of the angle. This allows atan2 to determine the angle's quadrant and return the correct angle within the range -π <= atan2() <= π.

Quadrant Resolution

The key difference between atan and atan2 is in how they resolve the quadrant of the angle. atan assumes the input came from the first or fourth quadrant, while atan2 considers the signs of both the sine and cosine to determine the correct quadrant.

Syntax

double atan(double radians);
double atan2(double y, double x);

Example

Consider an angle α with a tangent of 1. Using atan() alone, we cannot determine whether α is in the first or third quadrant. However, using atan2(), we can retrieve the correct angle:

double angle = atan2(sin(alpha), cos(alpha));

Additional Note

atan2() is particularly useful in vector calculations, where it can be used to find the angle of a vector in Cartesian coordinates.

Conclusion

While atan is sufficient for certain applications that only require angles within the first or fourth quadrant, atan2 provides a more comprehensive solution by resolving the angle's quadrant and returning the correct angle within the entire range [-π, π].

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