W3cubDocs

ccosf, ccos, ccosl

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

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

Example

#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)