TRIG(3M)TRIG(3M) NAME acos, asin, atan, atan2, cos, sin, tan, acosf, asinf, atanf, atan2f, cosf, sinf, tanf, acosl, asinl, atanl, atan2l, cosl, sinl, tanl, cacos, casin, catan, ccos, csin, ctan, cacosf, casinf, catanf, ccosf, csinf, csinf, ctanf, cacosl, casinl, catanl, ccosl, csinl, ctanl - trigonometric functions and their inverses SYNOPSIS #include <math.h> double acos(double x); float acosf(float x); long double acosl(long double x); double asin(double x); float asinf(float x); long double asinl(long double x); double atan(double x); float atanf(float x); long double atanl(long double x); double atan2(double y, double x); float atan2f(float y, float x); long double atan2l(long double y long double x); double cos(double x); float cosf(float x); long double cosl(long double x); double sin(double x); float sinf(float x); long double sinl(long double x); double tan(double x); float tanf(float x); long double tanl(long double x); #include <complex.h> double complex cacos(double complex z); float complex cacosf(float complex z); long double complex cacosl(long double complex z); double complex casin(double complex z); float complex casinf(float complex z); long double complex casinl(long double complex z); double complex catan(double complex z); float complex catanf(float complex z; long double complex catanl(long double complex z); double complex ccos(double complex z); float complex ccosf(float complex z); long double complex ccosl(long double complex z); double complex csin(double complex z); float complex csinf(float complex z); long double complex csinl(long double complex z); double complex ctan(double complex z); float complex ctanf(float complex z; long double complex ctanl(long double complex z); DESCRIPTION The complex functions are available only in libm and libmx for programs compiled with -n32 or -64. The single-precision and long double-precision routines listed above are only available in the standard math library, -lm, and in -lmx. Alternate entries exist for several routines. The following lists those routines with their ANSI standard name and the alternate entry name: ANSI standard name Alternate name sinf fsin asinf fasin cosf fcos acosf facos atanf fatan tanf ftan atan2f fatan2 cosl qcos acosl qacos asinl qasin atanl qatan atan2l qatan2 sinl qsin tanl qtan sin, cos and tan return trigonometric functions of radian arguments x for double data types. 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 inverse 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 casin functions return the complex inverse sine value. The csin functions return the complex sine value. The acos routines return the inverse 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 ccos functions compute the complex cosine of z. The cacos functions return the complex inverse cosine value. The atan routines return the inverse 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 inverse tangent 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. The ctan functions compute the complex tangent of z. The catan functions compute the complex inverse tangent of z. NOTES Functions in the standard math library (libm.a) are referred to as -lm; functions 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 return zero if both arguments are zero. The -lm versions also set errno to EDOM. An exception is the -lm43 versions, which return the following results: atan2(0.0, 0.0) = 0.0 atan2(-0.0, 0.0) = -0.0 atan2(0.0, -0.0) = pi This matches the proposed ANSI C9X Standard. The -lm versions also set errnor to EDOM for these arguments. See matherr(3M) for a description of error handling for -lmx functions. The 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 ULP 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 were optional according to the ANSI C Programming Language Specification ISO/IEC 9899 : 1990 (E) and are no longer optional according to ISO/IEC 9899: 1999(E). Long double functions are named 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 following are reasons for assigning a value to atan2(0,0): * 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. * atan2 is used mostly to convert from rectangular (x,y) to polar (r,theta) if 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 as follows: r:= hypot(x,y); . . . := sqrt(x*x+y*y) theta:= atan2(y,x) * The previous formulas do not have to 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. 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); This is the case 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) The Fortran version of these routines: sin(3F), cos(3F), tan(3F), asin(3F), acos(3F), atan(3F), atan2(3F)