ATAN2(3) BSD Library Functions Manual ATAN2(3)[top]NAMEatan2— arc tangent function of two variablesSYNOPSIS#include <math.h> double atan2(double y, double x);DESCRIPTIONTheatan2function computes the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of the return value.RETURN VALUESTheatan2function, if successful, returns the arc tangent of y/x in the range [-π, +π] radians. If both x and y are zero, the global variable errno is set to EDOM. On the VAX: atan2(y, x) := atan(y/x) if x > 0, sign(y)*(π - atan(|y/x|)) if x < 0, 0 if x = y = 0, or sign(y)*π/2 if x = 0 y.NOTESThe function atan2() defines "if x > 0," atan2(0, 0) = 0 on a VAX despite that previously atan2(0, 0) may have generated an error message. The reasons for assigning a value to atan2(0, 0) are these: 1. Programs that test arguments to avoid computing atan2(0, 0) must be indifferent to its value. Programs that require it to be invalid are vulnerable to diverse reactions to that inva‐ lidity on diverse computer systems. 2. The atan2() function is used mostly to convert from rectangu‐ lar (x,y) to polar (r,theta) coordinates that must satisfy x = r∗cos theta and y = r∗sin theta. These equations are satis‐ fied when (x=0,y=0) is mapped to (r=0,theta=0) on a VAX. In general, conversions to polar coordinates should be computed thus: r := hypot(x,y); ... := sqrt(x∗x+y∗y) theta := atan2(y,x). 3. The foregoing formulas need not be altered to cope in a rea‐ sonable way with signed zeros and infinities on a machine that conforms to IEEE 754; the versions of hypot(3) and atan2() provided for such a machine are designed to handle all cases. That is why atan2(±0, -0) = ±π for instance. In general the formulas above are equivalent to these: r := sqrt(x∗x+y∗y); if r = 0 then x := copysign(1,x);SEE ALSOacos(3), asin(3), atan(3), cos(3), cosh(3), sin(3), sinh(3), tan(3), tanh(3), math(3),STANDARDSThe atan2() function conforms to ANSI X3.159-1989 (“ANSI C89”).BSDJune 4, 1993 BSD

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