# Section (3) cacosh

Section 3 Linux manual pages

## 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`)`;

Note Link with `−lm`.

## DESCRIPTION

These functions calculate 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.

## ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

 Interface Attribute Value `cacosh`(), `cacoshf`(), `cacoshl`() Thread safety MT-Safe

## CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

## 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>
, argv[0]);
exit(EXIT_FAILURE);
}

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

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

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

exit(EXIT_SUCCESS);
}
```

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