NAME

tan, tanf, tanl — tangent function

SYNOPSIS

#include <math.h>

double tan(double x);
float tanf(float x);
long double tanl(long double x);


DESCRIPTION

^[CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2024 defers to the ISO C standard.

These functions shall compute the tangent of their argument x, measured in radians.

An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

RETURN VALUE

Upon successful completion, these functions shall return the tangent of x.

If the correct value would cause underflow, ^[MXX]  and is not representable,  a range error may occur, and tan(), tanf(), and tanl() shall return ^[MXX]  0.0, or  (if IEC 60559 Floating-Point is not supported) an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

^[MX] If x is NaN, a NaN shall be returned.

If x is ±0, x shall be returned.

If x is ±Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.

^[MXX] If x is subnormal, x should be returned.
^[MX] If x is subnormal, a range error may occur and, if x is not returned, tan(), tanf(), and tanl() shall return an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

^[MXX] If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.

^[XSI] If the correct value would cause overflow, a range error shall occur and tan(), tanf(), and tanl() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively, with the same sign as the correct value of the function.

ERRORS

These functions shall fail if:

Domain Error

^[MX] The value of x is ±Inf.

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.

Range Error

^[XSI] The result overflows

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

These functions may fail if:

Range Error

The result underflows, ^[MX]  or the value of x is subnormal.

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

EXAMPLES

Taking the Tangent of a 45-Degree Angle

#include <math.h>
...
double radians = 45.0 * M_PI / 180;
double result;
...
result = tan (radians);

APPLICATION USAGE

There are no known floating-point representations such that for a normal argument, tan(x) is either overflow or underflow.

These functions may lose accuracy when their argument is near a multiple of ℼ/2 or is far from 0.0.

On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

RATIONALE

None.

FUTURE DIRECTIONS

None.

SEE ALSO

atan, feclearexcept, fetestexcept, isnan

XBD 4.23 Treatment of Error Conditions for Mathematical Functions, <math.h>

CHANGE HISTORY

First released in Issue 1. Derived from Issue 1 of the SVID.

Issue 5

The last two paragraphs of the DESCRIPTION were included as APPLICATION USAGE notes in previous issues.

Issue 6

The tanf() and tanl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

IEEE Std 1003.1-2001/Cor 1-2002, item XSH/TC1/D6/64 is applied, correcting the last paragraph in the RETURN VALUE section.

Issue 7

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0635 [68], XSH/TC1-2008/0636 [68], and XSH/TC1-2008/0637 [68] are applied.

Issue 8

Austin Group Defect 1382 is applied, rearranging the text describing the behavior when x is subnormal to avoid the need for two shading changes.