# csinf, csin, csinl

< c‎ | numeric‎ | complex

C
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Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
 ccos csin ctan
Hyperbolic functions

 Defined in header 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 #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.

## Contents

### 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)