# cacosf, cacos, cacosl

< c‎ | numeric‎ | complex

C
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Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
 cacos casin catan
Hyperbolic functions

 Defined in header  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  #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.

## Contents

### 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)