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
As shipped in IRIX 6.5. First release of IRIX 6.5.
NAME 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 SYNOPSIS #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); DESCRIPTION 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 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. DIAGNOSTICS 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. NOTES 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 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. SEE ALSO math(3M), hypot(3M), sqrt(3M), matherr(3M) AUTHOR Robert P. Corbett, W. Kahan, Stuart I. McDonald, Peter Tang and, for the codes for IEEE 754, Dr. Kwok-Choi Ng.