csinf, csin, csinl
From cppreference.com
C
Concurrency support (C11)
Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
Defined in header
<complex.h>
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.[edit] Parameters
z
-
complex argument
[edit] 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)
[edit] 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
-e-iz
2i
[edit] 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)
[edit] References
- C17 standard (ISO/IEC 9899:2018):
- 7.3.5.5 The csin functions (p: 138-139)
- 7.25 Type-generic math <tgmath.h> (p: 272-273)
- G.7 Type-generic math <tgmath.h> (p: 397)
- 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)
[edit] See also
C++ documentation for sin