When to Use `atan` vs `atan2` in C : Which Function Gives the Right Angle?

Distinguishing between atan and atan2 in C

C offers mathematical functions for trigonometric calculations, including atan and atan2. To understand their difference, let's examine the tangent function.

Tangent Function and Quadrants

The tangent of an angle α is defined as tan(α) = sin(α) / cos(α). However, ambiguities arise due to quadrants.

Quadrant	Angle Range	sin Sign	cos Sign	tan Sign
I	0 < α < π/2
II	π/2 < α < π		-	-
III	π < α < 3π/2	-	-
IV	3π/2 < α < 2π	-		-

atan Function

The atan function returns the arctangent of y/x, assuming x > 0. This restricts the output to quadrants I and IV (i.e., -π/2 ≤ atan() ≤ π/2).

atan2 Function

Unlike atan, the atan2 function takes two arguments, y and x, which represent the projections of a vector on the y- and x-axes, respectively.

atan2(y, x) calculates the arctangent of y/x, considering both the y and x coordinates separately. This resolves all four quadrants by adding π to the atan() result when the cosine is negative.

Practical Implications

atan(y/x) can only determine angles from quadrants I or IV, while atan2(y, x) captures the full information and resolves the correct angle in all quadrants.

Conclusion

In summary, atan provides limited information and assumes an angle within quadrants I or IV, whereas atan2 retrieves comprehensive data and determines the angle in all quadrants. If precise angle calculation across all quadrants is required, atan2 is the preferred choice.

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