csinf, csin, csinl - cppreference.com (original) (raw)

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.

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 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 =

[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