CodeCogs

arc sine function

You're viewing an older version of this page (#3424). View the current version.

Interface

#include <math.h> double asin ( double x ) long asinl ( long double x ) float asinf ( float x )

#include <complex.h> complex asin(complex x) double complex casin(complex x) float complex casinf(float complex x) long double complex casinl(long double complex x)

Description

The asin function computes the principal value of the arc sine of x in the range $[-1,1]$ , returning a value in the interval $[-\pi/2,+\pi/2]$ . The arc sine is also often called the inverse sine and is denoted by $\sin^{-1}(x)$ .

The complex inverse sine is defined by:

$\mathrm{asin}(x) = -i \log\left (i x + \sqrt{1-x^2} \right )$

(1)

Example 1

#include <stdio.h>
#include <math.h>

int main(void)
{
  double result, x = 0.289;
  result = asin(x);
  printf("The arc sin of %lf is %lf\n", x, result);
  return 0;
}

Output:

The arc sin of 0.289000 is 0.293182

Special Values

asin ( 0 ) returns 0.
asin ( x ) returns a NaN and raises the invalid floating-point exception for |x| > 1.

Standards

The asin function conforms to ISO/IEC 9899:1999(E).

Compatibility

<table class="compat"> <tr><th></th><th>DOS</th><th>UNIX</th><th>Windows</th><th>ANSI C</th><th>C++ only</th></tr> <tr><td>asinl</td><td>•</td><td></td><td>•</td><td></td><td></td></tr> <tr><td>asinf</td><td>•</td><td>•</td><td>•</td><td></td><td></td></tr> <tr><td>Real asin</td><td>•</td><td>•</td><td>•</td><td>•</td><td></td></tr> <tr><td>Complex asin</td><td>•</td><td></td><td>•</td><td></td><td>•</td></tr> <tr><td>Complex casin</td><td></td><td>•</td><td></td><td></td><td>•</td></tr> </table>

asin