TRIG(3M) TRIG(3M)
sin, cos, tan, asin, acos, atan, atan2, fsin, sinf, fcos, cosf, ftan,
tanf, fasin, asinf, facos, acosf, fatan, atanf, fatan2, atan2f, sinl,
cosl, tanl, asinl, acosl, atanl, atan2l - trigonometric functions and
their inverses
#include <math.h>
double sin(double x);
float fsin(float x);
float sinf(float x);
long double sinl(long double x);
double cos(double x);
float fcos(float x);
float cosf(float x);
long double cosl(long double x);
double tan(double x);
float ftan(float x);
float tanf(float x);
long double tanl(long double x);
double asin(double x);
float fasin(float x);
float asinf(float x);
long double asinl(long double x);
double acos(double x);
float facos(float x);
float acosf(float x);
long double acosl(long double x);
double atan(double x);
float fatan(float x);
float atanf(float x);
long double atanl(long double x);
double atan2(double y, double x);
float fatan2(float y, float x);
float atan2f(float y, float x);
long double atan2l(long double y, \
long double x);
The single-precision and long double-precision routines listed above are
only available in the standard math library, -lm, and in -lmx.
sin, cos and tan return trigonometric functions of radian arguments x for
double data types. fsin, fcos and ftan, and their ANSI-named
counterparts sinf, cosf and tanf return trigonometric functions of radian
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TRIG(3M) TRIG(3M)
arguments x for float data types. sinl, cosl and tanl do the same for
long double data types.
The asin routines return the arc sine in the range -pi/2 to pi/2. The
type of both the return value and the single argument are double for
asin, float for fasin and its ANSI-named counterpart asinf, and long
double for asinl.
The acos routines return the arc cosine in the range 0 to pi. The type
of both the return value and the single argument are double for acos,
float for facos and its ANSI-named counterpart acosf, and long double for
acosl.
The atan routines return the arc tangent in the range -pi/2 to pi/2. The
type of both the return value and the single argument are double for
atan, float for fatan and its ANSI-named counterpart atanf, and long
double for atanl.
The atan2 routines return the arctangent of y/x in the range -pi to pi
using the signs of both arguments to determine the quadrant of the return
value. Both the return value and the argument types are double for
atan2, float for fatan2 and its ANSI-named counterpart atan2f, and long
double for atan2l.
In the diagnostics below, functions in the standard math library libm.a,
are referred to as -lm versions, and those in the the BSD math library
libm43.a, are referred to as -lm43 versions. The -lm versions always
return the default Quiet NaN and set errno to EDOM when a NaN is used as
an argument. A NaN argument usually causes the -lm43 versions to return
the same argument. The -lm43 versions never set errno.
If |x| > 1 the -lm versions of the asin and acos functions set errno to
EDOM and return NaN. When the argument is greater than one, the return
value of the -lm43 versions is indeterminate.
The atan2 functions will return zero if both arguments are zero. The -lm
versions also set errno to EDOM. (Exception: the -lm43 versions return
the following results:
atan2(0.0, 0.0) = 0.0
atan2(-0.0, 0.0) = -0.0
atan2(0.0, -0.0) = pi
atan2(-0.0, -0.0) = -pi )
See matherr(3M) for a description of error handling for -lmx functions.
Single precision routines fsin, fcos, and ftan are accurate to within 1
ulp for arguments in the range -2**22 to 2**22. Double precision
routines sin, cos, and tan are accurate to within 2 ulps for arguments in
the range -2**28 to 2**28. Arguments larger than this lose precision
rapidly, but retain more than 20 bits precision out to +/-2**50 for the
TRIG(3M) TRIG(3M)
double routines.
Long double operations on this system are only supported in round to
nearest rounding mode (the default). The system must be in round to
nearest rounding mode when calling any of the long double functions, or
incorrect answers will result.
Users concerned with portability to other computer systems should note
that the long double and float versions of these functions are optional
according to the ANSI C Programming Language Specification ISO/IEC 9899 :
1990 (E).
Long double functions have been renamed to be compliant with the ANSI-C
standard, however to be backward compatible, they may still be called
with the double precision function name prefixed with a q.
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 invalidity on diverse
computer systems.
(2) atan2 is used mostly to convert from rectangular (x,y) to polar
(r,theta) coordinates that must satisfy x = r*cos theta and y = r*sin
theta. These equations are satisfied when (x=0,y=0) is mapped to
(r=0,theta=0) 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 reasonable
way with signed zeros and infinities on machines, such as SGI 4D
machines, that conform to IEEE 754; the versions of hypot and atan2
provided for such a machine are designed to handle all cases. That
is why atan2(_0,-0) = _pi, 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);
if x > 0 then theta := 2*atan(y/(r+x))
else theta := 2*atan((r-x)/y);
except if r is infinite then atan2 will yield an appropriate multiple of
pi/4 that would otherwise have to be obtained by taking limits.
math(3M), hypot(3M), sqrt(3M), matherr(3M)
Robert P. Corbett, W. Kahan, Stuart I. McDonald, Peter Tang and, for the
codes for IEEE 754, Dr. Kwok-Choi Ng.
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ATAN2(3F) ATAN2(3F)
atan2, datan2, qatan2, atan2d, datan2d, qatan2d - FORTRAN arctangent
intrinsic function
real r1, r2, r3
double precision dp1, dp2, dp3
real*16 qp1, qp2, qp3
real*4 r4, r5, r6
real*8 dp4, dp5, dp6
real*16 qp4, qp5, qp6
r3 = atan2(r1, r2)
dp3 = datan2(dp1, dp2)
dp3 = atan2(dp1, dp2)
qp3 = qatan2(qp1, qp2)
qp3 = atan2(qp1, qp2)
r6 = atan2d(r4, r5)
dp6 = datan2d(dp4, dp5)
dp6 = atan2d(dp4, dp5)
qp6 = qatan2d(qp4, qp5)
qp6 = atan2d(qp4, qp5)
atan2 returns the arctangent of arg1/arg2 as a real value. datan2
returns the double-precision arctangent of its double-precision
arguments. qatan2 returns the real*16 arctangent of its real*16
arguments. The generic form atan2 may be used with impunity with
double-precision or real*16 arguments. If the value of the first
argument of atan2, datan2, or qatan2 is positive, the result is positive.
If the value of the first argument is negative, the result is negative.
When the value of the first argument is positive/negative zero, the
result is positive/negative zero if the second argument is positive and
positive/negative Pi if the second argument is negative. If the value of
the second argument is zero, the absolute value of the result is Pi/2.
Both arguments must not have the value zero. The result of atan2,
datan2, and qatan2 is in radians and is in the range: -Pi <= result <=
Pi.
atan2d returns the arctangent of arg1/arg2 as a real*4 value. datan2d
returns the real*8 arctangent of its real*8 arguments. qatan2d returns
the real*16 arctangent of its real*16 arguments. The generic form atan2d
may be used with impunity with real*8 or real*16 arguments. If the value
of the first argument of atan2d, datan2d, or qatan2d is positive, the
result is positive. When the value of the first argument is zero, the
result is zero if the second argument is positive and 180.0 if the second
argument is negative. If the value of the first argument is negative,
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ATAN2(3F) ATAN2(3F)
the result is negative. If the value of the second argument is zero, the
absolute value of the result is 90.0 . Both arguments must not have the
value zero. The result of atan2d, datan2d, and qdatan2d is in degrees
and is in the range: -180 degrees <= result <= 180 degrees.
trig(3M).
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