---
name: "cacosh"
section: "3"
platform: "freebsd"
package: "base"
version: "16.0-CURRENT-20261027-61c70dc16a79"
release: "FreeBSD 16.0-CURRENT (2026-10-27)"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/cacos"
---

# cacosh(3)

complex inverse trigonometric and hyperbolic functions

Part of [cacos(3)](/cacos/3.md).

## NAME

**cacos**, **cacosf**, **cacosl**, **cacosh**, **cacoshf**, **cacoshl**, **casin**, **casinf**, **casinl**, **casinh**, **casinhf**, **casinhl**, **catan**, **catanf**, **catanl**, **catanh**, **catanhf**, **catanhl** – complex inverse trigonometric and hyperbolic functions

## LIBRARY

Math Library (libm, -lm)

## SYNOPSIS

**#include \<complex.h\>**

*double* *complex*\

**cacos**(*double complex z*);

*float* *complex*\

**cacosf**(*float complex z*);

*long* *double* *complex*\

**cacosl**(*long double complex z*);

*double* *complex*\

**cacosh**(*double complex z*);

*float* *complex*\

**cacoshf**(*float complex z*);

*long* *double* *complex*\

**cacoshl**(*long double complex z*);

*double* *complex*\

**casin**(*double complex z*);

*float* *complex*\

**casinf**(*float complex z*);

*long* *double* *complex*\

**casinl**(*long double complex z*);

*double* *complex*\

**casinh**(*double complex z*);

*float* *complex*\

**casinhf**(*float complex z*);

*long* *double* *complex*\

**casinhl**(*long double complex z*);

*double* *complex*\

**catan**(*double complex z*);

*float* *complex*\

**catanf**(*float complex z*);

*long* *double* *complex*\

**catanl**(*long double complex z*);

*double* *complex*\

**catanh**(*double complex z*);

*float* *complex*\

**catanhf**(*float complex z*);

*long* *double* *complex*\

**catanhl**(*long double complex z*);

## DESCRIPTION

The **cacos**(), **casin**(), and **catan**() functions compute the principal value of the inverse cosine, sine, and tangent of the complex number *z*, respectively. The **cacosh**(), **casinh**(), and **catanh**() functions compute the principal value of the inverse hyperbolic cosine, sine, and tangent. The **cacosf**(), **casinf**(), **catanf**() **cacoshf**(), **casinhf**(), and **catanhf**() functions perform the same operations in *float* precision. The **cacosl**(), **casinl**(), **catanl**() **cacoshl**(), **casinhl**(), and **catanhl**() functions perform the same operations in *long*, *double* precision.

There is no universal convention for defining the principal values of these functions. The following table gives the branch cuts, and the corresponding ranges for the return values, adopted by the C language.

| | | |
| --- | --- | --- |
| **Function** | **Branch** **Cut(s)** | **Range** |
| cacos | (-, -1) ∪ (1,) | \[0,\] |
| casin | (-, -1) ∪ (1,) | \[-/2, /2\] |
| catan | (-\*I, -I) ∪ (I, \*I) | \[-/2, /2\] |
| cacosh | (-, 1) | \[-\*I, \*I\] |
| casinh | (-\*I, -I) ∪ (I, \*I) | \[-/2\*I, /2\*I\] |
| catanh | (-, -1) ∪ (1,) | \[-/2\*I, /2\*I\] |

## SEE ALSO

[ccos(3)](/ccos/3.md), [ccosh(3)](/ccosh/3.md), [complex(3)](/complex/3.md), [cos(3)](/cos/3.md), [math(3)](/math/3.md), [sin(3)](/sin/3.md), [tan(3)](/tan/3.md)

## STANDARDS

These functions conform to ISO/IEC 9899:1999 (“ISO C99”).