csinf, csin, csinl

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 = e iz -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)

Language
headers
Type support
Dynamic memory management
Error handling
Program utilities
Variadic function support
Date and time utilities
Strings library
Algorithms
Numerics
Input/output support
Localization support
Thread support (C11)
Atomic operations (C11)
Technical Specifications

Common mathematical functions
Floating-point environment
Complex number arithmetics
Random number generation
Type-generic math

ccosccosfccosl (C99)(C99)(C99)	computes the complex cosine (function)
ctanctanfctanl (C99)(C99)(C99)	computes the complex tangent (function)
casincasinfcasinl (C99)(C99)(C99)	computes the complex arc sine (function)
sinsinfsinl (C99)(C99)	computes sine ( $sin(x)$ ) (function)
C++ documentation for sin