tan, tanf, tanl

Defined in header `<math.h>`
float tanf( float arg );	(1)	(since C99)
double tan( double arg );	(2)
long double tanl( long double arg );	(3)	(since C99)
_Decimal32 tand32( _Decimal32 arg );	(4)	(since C23)
_Decimal64 tand64( _Decimal64 arg );	(5)	(since C23)
_Decimal128 tand128( _Decimal128 arg );	(6)	(since C23)
Defined in header `<tgmath.h>`
#define tan( arg )	(7)	(since C99)

1-6) Computes the tangent of arg (measured in radians).

7) Type-generic macro: If the argument has type long double, (3) (tanl) is called. Otherwise, if the argument has integer type or the type double, (2) (tan) is called. Otherwise, (1) (tanf) is called. If the argument is complex, then the macro invokes the corresponding complex function (ctanf, ctan, ctanl).

The functions (4-6) are declared if and only if the implementation predefines __STDC_IEC_60559_DFP__ (i.e. the implementation supports decimal floating-point numbers).

(since C23)

Parameters

arg

floating-point value representing angle in radians

Return value

If no errors occur, the tangent of arg (tan(arg)) is returned.

The result may have little or no significance if the magnitude of arg is large.

(until C99)

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

if the argument is ±0, it is returned unmodified;
if the argument is ±∞, NaN is returned and FE_INVALID is raised;
if the argument is NaN, NaN is returned.

Notes

The case where the argument is infinite is not specified to be a domain error in C, but it is defined as a domain error in POSIX.

The function has mathematical poles at π(1/2 + n); however no common floating-point representation is able to represent π/2 exactly, thus there is no value of the argument for which a pole error occurs.

Example

#include <errno.h>
#include <fenv.h>
#include <math.h>
#include <stdio.h>
 
#ifndef __GNUC__
#pragma STDC FENV_ACCESS ON
#endif
 
int main(void)
{
    const double pi = acos(-1);
 
    // typical usage
    printf("tan(pi*1/4) = %+f\n", tan(pi * 1 / 4)); //   45 deg
    printf("tan(pi*3/4) = %+f\n", tan(pi * 3 / 4)); //  135 deg
    printf("tan(pi*5/4) = %+f\n", tan(pi * 5 / 4)); // -135 deg
    printf("tan(pi*7/4) = %+f\n", tan(pi * 7 / 4)); //  -45 deg
 
    // special values
    printf("tan(+0) = %f\n", tan(0.0));
    printf("tan(-0) = %f\n", tan(-0.0));
 
    // error handling
    feclearexcept(FE_ALL_EXCEPT);
    printf("tan(INFINITY) = %f\n", tan(INFINITY));
    if (fetestexcept(FE_INVALID))
        puts("    FE_INVALID raised");
}

Possible output:

tan(pi*1/4) = +1.000000
tan(pi*3/4) = -1.000000
tan(pi*5/4) = +1.000000
tan(pi*7/4) = -1.000000
tan(+0) = 0.000000
tan(-0) = -0.000000
tan(INFINITY) = -nan
    FE_INVALID raised

References

C23 standard (ISO/IEC 9899:2023):

7.12.4.7 The tan functions (p: TBD)
7.25 Type-generic math <tgmath.h> (p: TBD)
F.10.1.7 The tan functions (p: TBD)

C17 standard (ISO/IEC 9899:2018):

7.12.4.7 The tan functions (p: 175)
7.25 Type-generic math <tgmath.h> (p: 272-273)
F.10.1.7 The tan functions (p: 378)

C11 standard (ISO/IEC 9899:2011):

7.12.4.7 The tan functions (p: 240)
7.25 Type-generic math <tgmath.h> (p: 373-375)
F.10.1.7 The tan functions (p: 519)

C99 standard (ISO/IEC 9899:1999):

7.12.4.7 The tan functions (p: 220)
7.22 Type-generic math <tgmath.h> (p: 335-337)
F.9.1.7 The tan functions (p: 457)

C89/C90 standard (ISO/IEC 9899:1990):

4.5.2.7 The tan function

sinsinfsinl (C99)(C99)	computes sine (\({\small\sin{x} }\)sin(x)) (function)
coscosfcosl (C99)(C99)	computes cosine (\({\small\cos{x} }\)cos(x)) (function)
atanatanfatanl (C99)(C99)	computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
ctanctanfctanl (C99)(C99)(C99)	computes the complex tangent (function)
C++ documentation for `tan`