---
name: "cacosh"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/cacosh"
---

# cacosh(3)

complex arc hyperbolic cosine

## NAME

cacosh, cacoshf, cacoshl - complex arc hyperbolic cosine

## LIBRARY

Math library (*libm*, *-lm*)

## 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

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))
```

## ATTRIBUTES

For an explanation of the terms used in this section, see [**attributes**(7)](/attributes/7.md).

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

## STANDARDS

C11, POSIX.1-2008.

## HISTORY

C99, POSIX.1-2001. glibc 2.1.

## EXAMPLES

```
/* Link with "-lm" */
#include <complex.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.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(f), cimag(f));
    exit(EXIT_SUCCESS);
}
```

## SEE ALSO

[**acosh**(3)](/acosh/3.md), [**cabs**(3)](/cabs/3.md), [**ccosh**(3)](/ccosh/3.md), [**cimag**(3)](/cimag/3.md), [**complex**(7)](/complex/7.md)