acosh

acosh

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Calculates the inverse hyperbolic cosine of a number

 include <math.h> double acosh ( 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( )