# CACOSH

Section: Linux Programmer's Manual (3)
Updated: 2011-09-15

## NAME

cacosh, cacoshf, cacoshl - complex arc hyperbolic cosine

## SYNOPSIS

#include <complex.h>

double complex cacosh(double complex z);
float complex cacoshf(float complex z);
long double complex cacoshl(long double complex z);

## DESCRIPTION

The cacosh() function calculates the complex arc hyperbolic cosine of z. If y = cacosh(z), then z = ccosh(y). The imaginary part of y is chosen in the interval [-pi,pi]. The real part of y is chosen nonnegative.

One has:

```
cacosh(z) = 2 * clog(csqrt((z + 1) / 2) + csqrt((z - 1) / 2))
```

## VERSIONS

These functions first appeared in glibc in version 2.1.

C99.

## EXAMPLE

```/* Link with "-lm" */

#include <complex.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdio.h>

int
main(int argc, char *argv[])
{
double complex z, c, f;

if (argc != 3) {
fprintf(stderr, "Usage: %s <real> <imag>\n", argv[0]);
exit(EXIT_FAILURE);
}

z = atof(argv[1]) + atof(argv[2]) * I;

c = cacosh(z);
printf("cacosh() = %6.3f %6.3f*i\n", creal(c), cimag(c));

f = 2 * clog(csqrt((z + 1)/2) + csqrt((z - 1)/2));
printf("formula  = %6.3f %6.3f*i\n", creal(f2), cimag(f2));

exit(EXIT_SUCCESS);
}
```

acosh(3), cabs(3), ccosh(3), cimag(3), complex(7)

NAME
SYNOPSIS
DESCRIPTION
VERSIONS
CONFORMING TO
EXAMPLE