trig(S)                        6 January 1993                        trig(S)


 Name

    trig: acos, asin, atan, atan2, cos, sin, tan - trigonometric functions

 Syntax


    cc  . . .  -lm


    #include <math.h>

    double acos (x)
    double x;

    double asin (x)
    double x;

    double atan (x)
    double x;

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

    double cos (x)
    double x;

    double sin (x)
    double x;

    double tan (x)
    double x;


 Description

    The acos routine computes the arc cosine of x in the range of [0, PI]
    radians.  Specify x in the range of -1 to 1. Zero is returned on unsuc-
    cessful completion and errno indicates the error, or NaN (not a number)
    is returned and errno may be set to indicate the error. (NaN is defined
    in /usr/include/nan.h and is detected with the isnan(S) routine.)

    The asin routine returns the arc sine of x in the range of [-PI/2, PI/2]
    radians. Specify x in range of -1 to 1. Zero is returned on unsuccessful
    completion and errno indicates the error, or NaN is returned and errno
    may indicate the error.

    The atan routine returns the arc tangent of x in the range [-PI/2, PI/2]
    radians. Otherwise errno indicates the error or NaN is returned.

    The atan2 routine returns the arc tangent of y/x in the range of
    (-PI, PI].  Zero is returned on unsuccessful completion with errno indi-
    cating the error, or NaN is returned and errno may indicate the error.

    The cos routine returns the cosine of x measured in radians on successful
    completion. Otherwise, errno is set to indicate the error or NaN is
    returned. The cos routine may lose accuracy when its argument is far from
    zero.

    The sin routine returns the sine of its argument x measured in radians
    upon successful completion. Otherwise, errno is set to indicate the error
    or NaN is returned. The sin routine may lose accuracy when its argument
    is far from zero. When the sin routine fails, errno is set to one of:


    [EDOM]      The value of x is NaN, or x is +-HUGEVAL.

    [ERANGE]    The magnitude of x is such that total or partial loss of sig-
                nificance resulted.

    The tan routine returns the tangent of x measured in radians on success-
    ful completion.  Otherwise, errno indicates the error or NaN is returned.
    The tan routine may lose accuracy when its argument is far from zero.

    The tan routine may fail if:


    [EDOM]      The value of x is NaN.

    [ERANGE]    The value to be returned would have caused overflow or under-
                flow, or the magnitude of x is such that total or partial
                loss of signal would result.


 Note

    Before checking for errors, set errno to zero. If a value appears in
    errno or if the routine returns NaN, an error occurred.

 Diagnostics

    sin, cos, and tan lose accuracy when their argument is far from zero.
    For arguments sufficiently large, these functions return zero when there
    would otherwise be a complete loss of significance.  In this case a mes-
    sage indicating TLOSS error is printed on the standard error output.  For
    less extreme arguments causing partial loss of significance, a PLOSS
    error is generated but no message is printed.  In both cases, errno is
    set to ERANGE.

    If the magnitude of the argument of asin or acos is greater than one, or
    if both arguments of atan2 are zero, zero is returned and errno is set to
    EDOM.  In addition, a message indicating DOMAIN error is printed on the
    standard error output.

    These error-handling procedures may be changed with the function
    matherr(S).

 See also

    matherr(S)

 Standards conformance

    acos, asin, atan, atan2, cos, sin, and tan
    AT&T SVID Issue 2;
    X/Open Portability Guide, Issue 3, 1989;
    ANSI X3.159-1989 Programming Language -- C;
    IEEE POSIX Std 1003.1-1990 System Application Program Interface (API) [C
    Language] (ISO/IEC 9945-1);
    and NIST FIPS 151-1.