# ccosf, ccos, ccosl

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< c‎ | numeric‎ | complex

Defined in header `<complex.h>` |  |
float complex ccosf( float complex z ); | (1) | (since C99)
double complex ccos( double complex z ); | (2) | (since C99)
long double complex ccosl( long double complex z ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define cos( z ) | (4) | (since C99)

1-3) Computes the complex cosine of `z`.
4) Type-generic macro: If `z` has type long double complex, `ccosl` is called. if `z` has type double complex, `ccos` is called, if `z` has type float complex, `ccosf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (cosf, cos, cosl). If `z` is imaginary, then the macro invokes the corresponding real version of the function cosh, implementing the formula cos(iy) = cosh(y), and the return type is real.

### Parameters

z | - | complex argument

### Return value

If no errors occur, the complex cosine of `z` is returned.

Errors and special cases are handled as if the operation is implemented by ccosh(I*z).

### Notes

The cosine is an entire function on the complex plane, and has no branch cuts.

Mathematical definition of the cosine is cos z =

eiz +e-iz
2

### Example

Run this code

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

    int main(void)
    {
        double complex z = ccos(1);  // behaves like real cosine along the real line
        printf("cos(1+0i) = %f%+fi ( cos(1)=%f)\n", creal(z), cimag(z), cos(1));

        double complex z2 = ccos(I); // behaves like real cosh along the imaginary line
        printf("cos(0+1i) = %f%+fi (cosh(1)=%f)\n", creal(z2), cimag(z2), cosh(1));
    }

Output:

    cos(1+0i) = 0.540302-0.000000i ( cos(1)=0.540302)
    cos(0+1i) = 1.543081-0.000000i (cosh(1)=1.543081)

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.3.5.4 The ccos functions (p: 191)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - G.7 Type-generic math <tgmath.h> (p: 545)

- C99 standard (ISO/IEC 9899:1999):

  - 7.3.5.4 The ccos functions (p: 173)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - G.7 Type-generic math <tgmath.h> (p: 480)

### See also

csin csinf csinl (C99)(C99)(C99) | computes the complex sine (function)
ctan ctanf ctanl (C99)(C99)(C99) | computes the complex tangent (function)
cacos cacosf cacosl (C99)(C99)(C99) | computes the complex arc cosine (function)
cos cosf cosl (C99)(C99) | computes cosine (cos(x)) (function)

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