cacos(3)

💖 cacos(3) — bestie's guide to the complex arc cosine 💖

okay so picture this: you're deep in <complex.h> land, you need the arc cosine of a complex number, and you open the man page. that's this page. welcome. come sit with me. 🌸

this is the Library Functions Manual entry for cacos, and it's giving very much "math girlies rise up" energy. three flavors, one vibe. let's go. ✨

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📚 LIBRARY

this lives in the Math library, aka libm, and yeah you're gonna need to link it with -lm. no cap.

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🎀 SYNOPSIS

#include <complex.h>

double complex cacos(double complex z);
float complex cacosf(float complex z);
long double complex cacosl(long double complex z);

three functions, three precisions, all eating the same snack. 💅

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🦋 DESCRIPTION

okay so these functions calculate the complex arc cosine of z. so simple, so clean.

here's the deal, fr fr: if y = cacos(z), then z = ccos(y). they're inverse besties. the way that works is chef's kiss. 🫶

and the real part of y is chosen in the interval [0,pi]. that's the rules, periodt.

also, one has:

cacos(z) = -i * clog(z + i * csqrt(1 - z * z))

which is honestly iconic. write it on your mirror. 💜

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👑 ATTRIBUTES

so there's this thing called attributes(7) and it explains all the terms used in this section — go read it if you want the lore. here's the tea for our three functions:

• cacos(), cacosf(), cacosl()
  • Attribute: Thread safety
  • Value: MT-Safe

meaning: thread safe. run it everywhere. she's built different. 🔥

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🌈 STANDARDS

• C11
• POSIX.1-2008

that's it. standards, slayed. ⭐

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🕰️ HISTORY

• glibc 2.1 — the glow up era
• C99, POSIX.1-2001 — the origin story

ngl, she's been around a minute. 💀

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🧚 EXAMPLES

okay bestie, here's the whole demo. do NOT forget to link with "-lm" or nothing works and you'll be sad. 😭

/* 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;
    double complex i = I;

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

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

    c = cacos(z);

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

    f = -i * clog(z + i * csqrt(1 - z * z));

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

    exit(EXIT_SUCCESS);
}

so it takes <real> and <imag> as args, builds the complex number z, runs cacos(z), prints it, then also computes it with that formula from up top and prints that too — so you can literally watch them match in real time. main character energy. 👑

heads up: if argc != 3 it yells at you with the usage line and bails with exit(EXIT_FAILURE). feed it two numbers or don't bother. 🙈

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🔍 SEE ALSO

• ccos(3)
• clog(3)
• complex(7)

go read those, they're all in the same friend group. 🍓

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and that's the whole page, bestie!! 🥰 this was written by the Linux man-pages 6.20 girlies and dated 2026-02-08. wash your hands, link with -lm, and go compute something beautiful. mwah. 💅✨💖