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csinf, csin, csinl

From cppreference.com
< c‎ | numeric‎ | complex
Defined in header <complex.h>
float complex       csinf( float complex z );
(1) (since C99)
double complex      csin( double complex z );
(2) (since C99)
long double complex csinl( long double complex z );
(3) (since C99)
Defined in header <tgmath.h>
#define sin( z )
(4) (since C99)
1-3) Computes the complex sine of z.
4) 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.

Contents

[edit] Parameters

z - complex argument

[edit] Return value

If 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] Notes

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

Mathematical definition of the sine is sin z =
eiz
-e-iz
2i

[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] See also

(C99)(C99)(C99)
computes the complex cosine
(function) [edit]
(C99)(C99)(C99)
computes the complex tangent
(function) [edit]
(C99)(C99)(C99)
computes the complex arc sine
(function) [edit]
(C99)(C99)
computes sine (sin(x))
(function) [edit]