From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fcomplex%2Fcsin.html | 58 +++++++++++++++++++++++++++++++++ 1 file changed, 58 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fcsin.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcsin.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcsin.html b/devdocs/c/numeric%2Fcomplex%2Fcsin.html new file mode 100644 index 00000000..5e69806e --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcsin.html @@ -0,0 +1,58 @@ +

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 =

+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

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 (\({\small\sin{x} }\)sin(x))
(function)
C++ documentation for sin
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/complex/csin +

+
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