#define sin( z )
(4) (since C99)1-3) Computes the complex sine of z.
Type-generic macro: If
z
has type
long double complex,
csinl
is called. if
z
has type
double complex,
csin
is called, if
z
has type
float complex,
csinf
is called. If
z
is real or integer, then the macro invokes the corresponding real function (
sinf,
sin,
sinl). If
z
is imaginary, then the macro invokes the corresponding real version of the function
sinh, implementing the formula
sin(iy) = i ∙ sinh(y), and the return type of the macro is imaginary.
[edit] Parameters [edit] Return valueIf no errors occur, the complex sine of z.
Errors and special cases are handled as if the operation is implemented by -I * csinh(I*z)
[edit] NotesThe sine is an entire function on the complex plane, and has no branch cuts.
Mathematical definition of the sine is
sin z = [edit] Example#include <stdio.h>
#include <math.h>
#include <complex.h>
int main(void)
{
double complex z = csin(1); // behaves like real sine along the real line
printf("sin(1+0i) = %f%+fi ( sin(1)=%f)\n", creal(z), cimag(z), sin(1));
double complex z2 = csin(I); // behaves like sinh along the imaginary line
printf("sin(0+1i) = %f%+fi (sinh(1)=%f)\n", creal(z2), cimag(z2), sinh(1));
}
Output:
sin(1+0i) = 0.841471+0.000000i ( sin(1)=0.841471) sin(0+1i) = 0.000000+1.175201i (sinh(1)=1.175201)[edit] References
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