C in a Nutshell

Name

acosh

Synopsis

Calculates the inverse hyperbolic cosine of a number

include <math.h>
doubleacosh( double x );
float acoshf( float x );
long double acoshl( long double x );

The acosh() functions return the non-negative number whose hyperbolic cosine is equal to the argument x. Because the hyperbolic cosine of any number is greater than or equal to 1, acosh() incurs a domain error if the argument is less than 1.

Example

double x, y1, y2;

puts("acosh(x) is equal to log( x + sqrt(x*x − 1))\n");
puts("For the argument x, enter some numbers greater than or equal to 1.0"
     "\n(type any letter to quit):");
while ( scanf("%lf", &x) == 1)
{
  errno = 0;
  y1 =acosh(x);
  if ( errno == EDOM)
  {
    perror("acosh");   break;
  }
  y2 = log( x + sqrt( x*x − 1));
  printf("x = %f;  acosh(x) = %f;  log(x + sqrt(x*x-1)) = %f\n", x, y1, y2);
}

This code produces the following output:

For the argument x, enter some numbers greater than or equal to 1.0
(type any letter to quit):
1.5
x = 1.500000;  acosh(x) = 0.962424;  log(x + sqrt(x*x-1)) = 0.962424
0.5
acosh: Numerical argument out of domain

See Also

Other hyperbolic trigonometry functions for real numbers: asinh(), atanh(), sinh(), cosh(), and tanh(); the hyperbolic cosine and inverse hyperbolic cosine functions for complex numbers: ccosh() and cacosh()