ATAN2(3) BSD Library Functions Manual ATAN2(3)NAMEatan2 — arc tangent function of two variables
atan2(double y, double x);
The atan2 function computes the principal value of the arc tangent of
y/x, using the signs of both arguments to determine the quadrant of the
The atan2 function, 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.
The 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
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),
The atan2() function conforms to ANSI X3.159-1989 (“ANSI C89”).
BSD June 4, 1993 BSD