asin, asinf, asinl

Defined in header <math.h>
float       asinf( float arg );
(1) (since C99)
double      asin( double arg );
long double asinl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define asin( arg )
(4) (since C99)
1-3) Computes the principal values of the arc sine of arg.
4) Type-generic macro: If the argument has type long double, asinl is called. Otherwise, if the argument has integer type or the type double, asin is called. Otherwise, asinf is called. If the argument is complex, then the macro invokes the corresponding complex function (casinf, casin, casinl).


arg - floating point value

Return value

If no errors occur, the arc sine of arg (arcsin(arg)) in the range [-π/2 ; +π/2], is returned.

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.

Domain error occurs if arg is outside the range [-1.0; 1.0].

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

  • If the argument is ±0, it is returned unmodified
  • If |arg| > 1, a domain error occurs and NaN is returned.
  • if the argument is NaN, NaN is returned


#include <math.h>
#include <stdio.h>
#include <errno.h>
#include <fenv.h>
#include <string.h>
int main(void)
    printf("asin( 1.0) = %+f, 2*asin( 1.0)=%+f\n", asin(1), 2*asin(1));
    printf("asin(-0.5) = %+f, 6*asin(-0.5)=%+f\n", asin(-0.5), 6*asin(-0.5));
    // special values
    printf("asin(0.0) = %1f, asin(-0.0)=%f\n", asin(+0.0), asin(-0.0));
    // error handling 
    errno = 0; feclearexcept(FE_ALL_EXCEPT);
    printf("asin(1.1) = %f\n", asin(1.1));
    if(errno == EDOM) perror("    errno == EDOM");
    if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");

Possible output:

asin( 1.0) = +1.570796, 2*asin( 1.0)=+3.141593
asin(-0.5) = -0.523599, 6*asin(-0.5)=-3.141593
asin(0.0) = 0.000000, asin(-0.0)=-0.000000
asin(1.1) = nan
    errno == EDOM: Numerical argument out of domain
    FE_INVALID raised


  • C11 standard (ISO/IEC 9899:2011):
    • The asin functions (p: 238)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.1.2 The asin functions (p: 518)
  • C99 standard (ISO/IEC 9899:1999):
    • The asin functions (p: 219)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.1.2 The asin functions (p: 456)
  • C89/C90 standard (ISO/IEC 9899:1990):
    • The asin function

See also

computes arc cosine (\({\small\arccos{x} }\)arccos(x))
computes arc tangent (\({\small\arctan{x} }\)arctan(x))
computes arc tangent, using signs to determine quadrants
computes sine (\({\small\sin{x} }\)sin(x))
computes the complex arc sine
C++ documentation for asin

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