When Should I Use atan and When Should I Use atan2 in C ?

Identifying the Differences between atan and atan2 in C

In C , atan and atan2 are mathematical functions that calculate the angle from the tangent of an input. However, there are fundamental differences between these two functions that affect their output.

atan Function

atan(x) computes the arctangent of x, where x is the ratio of the sine and cosine of an angle. It returns an angle between -π/2 and π/2 (quadrants I and IV), regardless of the input. This is due to the fact that the division sin(α) / cos(α) cannot differentiate between quadrants I and III, or between quadrants II and IV.

atan2 Function

Unlike atan, atan2(y, x) takes two arguments, both of which represent the projections of a vector on the y-axis (y) and x-axis (x), respectively. These projections are the sine and cosine of the angle, respectively.

atan2 resolves all four quadrants by considering the sign of the cosine value. If the cosine is negative, it adds π to the result of atan(), effectively accounting for quadrants II and III.

Conclusion

While both atan and atan2 calculate the angle from the tangent, atan is limited to quadrants I and IV, as it only considers the ratio of sine and cosine. In contrast, atan2 provides more comprehensive information by considering both sine and cosine values, effectively resolving angles in all four quadrants. This makes atan2 a more versatile function for mathematical and computational purposes, particularly when dealing with angle computations that span multiple quadrants.

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