/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`

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```
• 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)

### See also

 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)

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