csinf, csin, csinl

< c‎ | numeric‎ | complex
 
C
 
Numerics
 
Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
csin
Hyperbolic functions
 
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

Run this code
#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)