tan, tanf, tanl

Defined in header <math.h>
float       tanf( float arg );
(1) (since C99)
double      tan( double arg );
long double tanl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define tan( arg )
(4) (since C99)
1-3) Computes the tangent of arg (measured in radians).
4) Type-generic macro: If the argument has type long double, tanl is called. Otherwise, if the argument has integer type or the type double, tan is called. Otherwise, tanf is called. If the argument is complex, then the macro invokes the corresponding complex function (ctanf, ctan, ctanl).


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


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.


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

Possible output:

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


  • C11 standard (ISO/IEC 9899:2011):
    • 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):
    • 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):
    • The tan function

See also

computes sine (\({\small\sin{x} }\)sin(x))
computes cosine (\({\small\cos{x} }\)cos(x))
computes arc tangent (\({\small\arctan{x} }\)arctan(x))
computes the complex tangent
C++ documentation for tan

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