# cacosh(3) — Linux manual page

```cacosh(3)               Library Functions Manual               cacosh(3)
```

## NAME         top

```       cacosh, cacoshf, cacoshl - complex arc hyperbolic cosine
```

## LIBRARY         top

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

## SYNOPSIS         top

```       #include <complex.h>

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

## DESCRIPTION         top

```       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         top

```       For an explanation of the terms used in this section, see
attributes(7).
┌─────────────────────────────────────┬───────────────┬─────────┐
│ Interface                           │ Attribute     │ Value   │
├─────────────────────────────────────┼───────────────┼─────────┤
│ cacosh(), cacoshf(), cacoshl()      │ Thread safety │ MT-Safe │
└─────────────────────────────────────┴───────────────┴─────────┘
```

## STANDARDS         top

```       C11, POSIX.1-2008.
```

## HISTORY         top

```       C99, POSIX.1-2001.  glibc 2.1.
```

## EXAMPLES         top

```       /* 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);
}
```

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