sin, sinf, sinl

Defined in header <math.h>
float       sinf( float arg );
(1) (since C99)
double      sin( double arg );
long double sinl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define sin( arg )
(4) (since C99)
1-3) Computes the sine of arg (measured in radians).
4) Type-generic macro: If the argument has type long double, sinl is called. Otherwise, if the argument has integer type or the type double, sin is called. Otherwise, sinf is called. If the argument is complex, then the macro invokes the corresponding complex function (csinf, csin, csinl).


arg - floating point value representing an angle in radians

Return value

If no errors occur, the sine of arg (sin(arg)) in the range [-1 ; +1], 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.

POSIX also specifies that in case of underflow, arg is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.


#include <stdio.h>
#include <math.h>
#include <errno.h>
#include <fenv.h>
int main(void)
    double pi = acos(-1);
    // typical usage
    printf("sin(pi/6) = %f\n", sin(pi/6));
    printf("sin(pi/2) = %f\n", sin(pi/2));
    printf("sin(-3*pi/4) = %f\n", sin(-3*pi/4));
    // special values
    printf("sin(+0) = %f\n", sin(0.0));
    printf("sin(-0) = %f\n", sin(-0.0));
    // error handling 
    printf("sin(INFINITY) = %f\n", sin(INFINITY));
    if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");

Possible output:

sin(pi/6) = 0.500000
sin(pi/2) = 1.000000
sin(-3*pi/4) = -0.707107
sin(+0) = 0.000000
sin(-0) = -0.000000
sin(INFINITY) = -nan
    FE_INVALID raised


  • C11 standard (ISO/IEC 9899:2011):
    • The sin functions (p: 239-240)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.1.6 The sin functions (p: 519)
  • C99 standard (ISO/IEC 9899:1999):
    • The sin functions (p: 220)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.1.6 The sin functions (p: 456)
  • C89/C90 standard (ISO/IEC 9899:1990):
    • The sin function

See also

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

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