cosh, coshf, coshl

Defined in header <math.h>
float       coshf( float arg );
(1) (since C99)
double      cosh( double arg );
long double coshl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define cosh( arg )
(4) (since C99)
1-3) Computes the hyperbolic cosine of arg.
4) Type-generic macro: If the argument has type long double, coshl is called. Otherwise, if the argument has integer type or the type double, cosh is called. Otherwise, coshf is called. If the argument is complex, then the macro invokes the corresponding complex function (ccoshf, ccosh, ccoshl).


arg - floating point value representing a hyperbolic angle

Return value

If no errors occur, the hyperbolic cosine of arg (cosh(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.

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, 1 is returned
  • If the argument is ±∞, +∞ is returned
  • if the argument is NaN, NaN is returned


For the IEEE-compatible type double, if |arg| > 710.5, then cosh(arg) overflows.


#include <stdio.h>
#include <math.h>
#include <errno.h>
#include <fenv.h>
int main(void)
    printf("cosh(1) = %f\ncosh(-1)= %f\n", cosh(1), cosh(-1));
    printf("log(sinh(1) + cosh(1))=%f\n", log(sinh(1)+cosh(1)));
    // special values
    printf("cosh(+0) = %f\ncosh(-0) = %f\n", cosh(0.0), cosh(-0.0));
    // error handling 
    errno=0; feclearexcept(FE_ALL_EXCEPT);
    printf("cosh(710.5) = %f\n", cosh(710.5));
    if(errno == ERANGE) perror("    errno == ERANGE");
    if(fetestexcept(FE_OVERFLOW)) puts("    FE_OVERFLOW raised");

Possible output:

cosh(1) = 1.543081
cosh(-1)= 1.543081
log(sinh(1) + cosh(1))=1.000000
cosh(+0) = 1.000000
cosh(-0) = 1.000000
cosh(710.5) = inf
    errno == ERANGE: Numerical result out of range
    FE_OVERFLOW raised


  • C17 standard (ISO/IEC 9899:2018):
    • The cosh functions (p: 176)
    • 7.25 Type-generic math <tgmath.h> (p: 272-273)
    • F.10.2.4 The cosh functions (p: 379)
  • C11 standard (ISO/IEC 9899:2011):
    • The cosh functions (p: 241)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.2.4 The cosh functions (p: 520)
  • C99 standard (ISO/IEC 9899:1999):
    • The cosh functions (p: 222)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.2.4 The cosh functions (p: 457)
  • C89/C90 standard (ISO/IEC 9899:1990):
    • The cosh function

See also

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

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