/C

# cacosf, cacos, cacosl

Defined in header `<complex.h>`
`float complex       cacosf( float complex z );`
(1) (since C99)
`double complex      cacos( double complex z );`
(2) (since C99)
`long double complex cacosl( long double complex z );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define acos( z )`
(4) (since C99)
1-3) Computes the complex arc cosine of `z` with branch cuts outside the interval [−1,+1] along the real axis.
4) Type-generic macro: If `z` has type `long double complex`, `cacosl` is called. if `z` has type `double complex`, `cacos` is called, if `z` has type `float complex`, `cacosf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (`acosf`, `acos`, `acosl`). If `z` is imaginary, then the macro invokes the corresponding complex number version.

### Parameters

 z - complex argument

### Return value

If no errors occur, complex arc cosine of `z` is returned, in the range [0 ; ∞) along the real axis and in the range [−iπ ; iπ] along the imaginary axis.

### Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• `cacos(conj(z)) == conj(cacos(z))`
• If `z` is `±0+0i`, the result is `π/2-0i`
• If `z` is `±0+NaNi`, the result is `π/2+NaNi`
• If `z` is `x+∞i` (for any finite x), the result is `π/2-∞i`
• If `z` is `x+NaNi` (for any nonzero finite x), the result is `NaN+NaNi` and `FE_INVALID` may be raised.
• If `z` is `-∞+yi` (for any positive finite y), the result is `π-∞i`
• If `z` is `-∞+yi` (for any positive finite y), the result is `+0-∞i`
• If `z` is `-∞+∞i`, the result is `3π/4-∞i`
• If `z` is `+∞+∞i`, the result is `π/4-∞i`
• If `z` is `±∞+NaNi`, the result is `NaN±∞i` (the sign of the imaginary part is unspecified)
• If `z` is `NaN+yi` (for any finite y), the result is `NaN+NaNi` and `FE_INVALID` may be raised
• If `z` is `NaN+∞i`, the result is `NaN-∞i`
• If `z` is `NaN+NaNi`, the result is `NaN+NaNi`

### Notes

Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventially placed at the line segments (-∞,-1) and (1,∞) of the real axis. The mathematical definition of the principal value of arc cosine is acos z =

 1 2
π + iln(iz + 1-z2
)

For any z, acos(z) = π - acos(-z).

### Example

```#include <stdio.h>
#include <math.h>
#include <complex.h>

int main(void)
{
double complex z = cacos(-2);
printf("cacos(-2+0i) = %f%+fi\n", creal(z), cimag(z));

double complex z2 = cacos(conj(-2)); // or CMPLX(-2, -0.0)
printf("cacos(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));

// for any z, acos(z) = pi - acos(-z)
double pi = acos(-1);
double complex z3 = ccos(pi-z2);
printf("ccos(pi - cacos(-2-0i) = %f%+fi\n", creal(z3), cimag(z3));
}```

Output:

```cacos(-2+0i) = 3.141593-1.316958i
cacos(-2-0i) (the other side of the cut) = 3.141593+1.316958i
ccos(pi - cacos(-2-0i) = 2.000000+0.000000i```

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.3.5.1 The cacos functions (p: 190)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.1.1 The cacos functions (p: 539)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.5.1 The cacos functions (p: 172)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.1.1 The cacos functions (p: 474)
• G.7 Type-generic math <tgmath.h> (p: 480)

 casincasinfcasinl (C99)(C99)(C99) computes the complex arc sine (function) catancatanfcatanl (C99)(C99)(C99) computes the complex arc tangent (function) ccosccosfccosl (C99)(C99)(C99) computes the complex cosine (function) acosacosfacosl (C99)(C99) computes arc cosine (arccos(x)) (function) C++ documentation for `acos`