| 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.Parameters
| z | - | complex argument |
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).
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 |
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)
References
- C11 standard (ISO/IEC 9899:2011):
- 7.3.5.5 The csin functions (p: 191-192)
- 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):
- 7.3.5.5 The csin functions (p: 173)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- G.7 Type-generic math <tgmath.h> (p: 480)
See also
| (C99)(C99)(C99) | computes the complex cosine (function) |
| (C99)(C99)(C99) | computes the complex tangent (function) |
| (C99)(C99)(C99) | computes the complex arc sine (function) |
| (C99)(C99) | computes sine (sin(x)) (function) |
C++ documentation for sin | |
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