trig(3M)

NAME

sin, cos, tan, asin, acos, atan, atan2, sinf, cosf, tanf, asinf, acosf, atanf, atan2f − trigonometric functions

SYNOPSIS

#include <math.h>

double sin (x)
double x;

double cos (x)
double x;

double tan (x)
double x;

double asin (x)
double x;

double acos (x)
double x;

double atan (x)
double x;

double atan2 (y, x)
double x, y;

For Series 1000, 3000, and 4000 Systems:

float sinf (float x)

float cosf (float x)

float tanf (float x)

float asinf (float x)

float acosf (float x)

float atanf (float x)

float atan2f (float y, float x)

DESCRIPTION

Sin, sinf, cos, cosf, tan, and tanf return, respectively, the sine, cosine, and tangent of their argument, x, measured in radians.

Asin and asinf return the arcsine of x, in the range −PI/2 to PI/2.

Acos and acosf return the arccosine of x, in the range 0 to PI.

Atan and atanf return the arctangent of x, in the range −PI/2 to PI/2.

Atan2 and atan2f 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.

DIAGNOSTICS

For the double precision functions: Sin, cos, and tan lose accuracy when their argument is far from zero. For arguments sufficiently large, these functions generate a TLOSS error when there would be a complete loss of significance. For less extreme arguments causing partial loss of significance, a PLOSS error is generated.

SIN,COS:	result	errno
total loss	0.0	ERANGE	TLOSS error message
partial loss	sin(x),cos(x)	ERANGE	no message
x = infinity	qNaN	EDOM	no message
x = NaN	qNaN	EDOM	no message

TAN:	result	errno
total loss	0.0	ERANGE	TLOSS mess.
partial loss	tan(x)	ERANGE	no message
x ~ pi/2 (Ser 1000, 3000, 4000)	+infinity	EDOM	no message
x = infinity	qNaN	EDOM	no message
x = NaN	qNaN	EDOM	no message

ASIN,ACOS:	result	errno
\|x\| > 1	0.0	EDOM	DOMAIN error message
x = infinity	qNaN	EDOM	no message
x = NaN	qNaN	EDOM	no message

ATAN:	result	errno
x = +infinity	+pi/2	not set	no message
x = -infinity	-pi/2	not set	no message
x = NaN	qNaN	EDOM	no message

ATAN2:	result	errno
x = 0.0, y = 0.0	0.0	EDOM	DOMAIN error
x = 0.0, y < 0.0	-pi/2	not set	no message
x = 0.0, y > 0.0	+pi/2	not set	no message
x < 0.0, y = 0.0	+pi	not set	no message
x > 0.0, y = 0.0	0.0	not set	no message
overflow, y < 0.0	-pi/2	not set	no message
overflow, y > 0.0	+pi/2	not set	no message
underflow, x > 0.0	0.0	not set	no message
underflow, x < 0.0, y < 0.0	-pi	not set	no message
underflow, x < 0.0, y > 0.0	+pi	not set	no message
x = infinity	qNaN	EDOM	no message
x = NaN or y = NaN	qNaN	EDOM	no message

These error-handling procedures may be changed with the matherr(3M) function, if the program is not linked in the ANSI C conforming mode (−Xc). See hc(1) for more information about compilation modes.

If the program is linked one of the ANSI C compilation modes, messages will not be produced under any circumstances.

For the single precision functions: Sinf, cosf, and tanf lose accuracy when their argument is far from zero. For arguments sufficiently large, these functions generate a TLOSS error when there would be a complete loss of significance. For less extreme arguments causing partial loss of significance, a PLOSS error is generated.

SINF,COSF:	result	errno
total loss	qNaN	EDOM	no message
x = infinity	qNaN	EDOM	no message
x = NaN	qNaN	EDOM	no message

TANF:	result	errno
total loss	qNaN	TLOSS	no message
partial loss	tanf(x)	PLOSS	no message
x ~ pi/2	+infinity	DOMAIN	no message
x = infinity	qNaN	DOMAIN	no message
x = NaN	qNaN	DOMAIN	no message

ASINF,ACOSF:	result	errno
\|x\| > 1	qNaN	DOMAIN	no message
x = infinity	qNaN	DOMAIN	no message
x = NaN	qNaN	DOMAIN	no message

ATANF:	result	errno
x = +infinity	+pi/2	not set	no message
x = -infinity	-pi/2	not set	no message
x = NaN	qNaN	EDOM	no message

ATAN2F:	result	errno
x = 0.0, y = 0.0	qNaN	DOMAIN	no message
x = 0.0, y < 0.0	-pi/2	not set	no message
x = 0.0, y > 0.0	+pi/2	not set	no message
x < 0.0, y = 0.0	+pi	not set	no message
x > 0.0, y = 0.0	0.0	not set	no message
overflow, y < 0.0	-pi/2	not set	no message
overflow, y > 0.0	+pi/2	not set	no message
underflow, x > 0.0	0.0	not set	no message
underflow, x < 0.0, y < 0.0	-pi	not set	no message
underflow, x < 0.0, y > 0.0	+pi	not set	no message
x = infinity	qNaN	EDOM	no message
x = NaN or y = NaN	qNaN	EDOM	no message

If the program is linked in one of the ANSI C compilation modes, tanf, asinf, acosf, and atan2f will set errno to EDOM instead of DOMAIN for domain errors.

The matherr(3M) function has no effect on the single precision functions.

PERFORMANCE IMPROVEMENTS

These functions check the integrity of their arguments for mathematical validity and conformance to the IEEE Floating-Point Arithmetic standard’s definition of numbers. They also maintain high accuracy of computations through occasional use of higher precision arithmetic and lengthier computations designed to minimize round-off errors. The library libm.a contains these robust functions. An alternate math library, libM.a, offers increased performance at the expense of argument checking and accuracy. The checks for mathematical validity and IEEE numbers are not performed on these functions in this additional library. Checks at the boundary conditions of minimum and maximum representable values, however, are conducted. The accuracy losses are usually never more than 1-bit differences when compared with the robust versions. This alternate library is intended for use when the characteristics of the arguments are well-understood and higher performance is preferred over increased accuracy. One consequence of these less-robust functions is that erroneous arguments are not caught and may produce meaningless answers.

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