csinf, csin, csinl

 

C

Language

Headers

Type support

Program utilities

Variadic function support

Error handling

Dynamic memory management

Date and time utilities

Strings library

Algorithms

Numerics

Input/output support

Localization support

Atomic operations (C11)

Thread support (C11)

Technical Specifications

 

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

 

Complex number arithmetic

Types and the imaginary constant
complex _Complex_I CMPLX	imaginary _Imaginary_I I
Manipulation
cimag creal carg	cabs conj cproj
Power and exponential functions
cexp clog	cpow csqrt
Trigonometric functions
ccos csin ctan	cacos casin catan
Hyperbolic functions
ccosh csinh ctanh	cacosh casinh catanh

 

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

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)