sinh, sinhf, sinhl

Defined in header <math.h>
float       sinhf( float arg );
(1) (since C99)
double      sinh( double arg );
long double sinhl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define sinh( arg )
(4) (since C99)
1-3) Computes hyperbolic sine of arg.
4) Type-generic macro: If the argument has type long double, sinhl is called. Otherwise, if the argument has integer type or the type double, sinh is called. Otherwise, sinhf is called. If the argument is complex, then the macro invokes the corresponding complex function (csinhf, csinh, csinhl).


arg - floating point value representing a hyperbolic angle

Return value

If no errors occur, the hyperbolic sine of arg (sinh(arg), or earg-e-arg/2) is returned.

If a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.

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 or ±∞, it is returned unmodified
  • if the argument is NaN, NaN is returned


POSIX 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)
    printf("sinh(1) = %f\nsinh(-1)=%f\n", sinh(1), sinh(-1));
    printf("log(sinh(1) + cosh(1))=%f\n", log(sinh(1)+cosh(1)));
    // special values
    printf("sinh(+0) = %f\nsinh(-0)=%f\n", sinh(0.0), sinh(-0.0));
    // error handling 
    errno=0; feclearexcept(FE_ALL_EXCEPT);
    printf("sinh(710.5) = %f\n", sinh(710.5));
    if(errno == ERANGE) perror("    errno == ERANGE");
    if(fetestexcept(FE_OVERFLOW)) puts("    FE_OVERFLOW raised");

Possible output:

sinh(1) = 1.175201
log(sinh(1) + cosh(1))=1.000000
sinh(+0) = 0.000000
sinh(710.5) = inf
    errno == ERANGE: Numerical result out of range
    FE_OVERFLOW raised


  • C17 standard (ISO/IEC 9899:2018):
    • The sinh functions (p: 176)
    • 7.25 Type-generic math <tgmath.h> (p: 272-273)
    • F.10.2.5 The sinh functions (p: 379)
  • C11 standard (ISO/IEC 9899:2011):
    • The sinh functions (p: 241-242)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.2.5 The sinh functions (p: 520)
  • C99 standard (ISO/IEC 9899:1999):
    • The sinh functions (p: 222)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.2.5 The sinh functions (p: 457)
  • C89/C90 standard (ISO/IEC 9899:1990):
    • The sinh function

See also

computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x))
computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x))
computes inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x))
computes the complex hyperbolic sine
C++ documentation for sinh

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