cacosh(3) Library Functions Manual cacosh(3)

# 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).

 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);
}```