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%2Fcasin.html | 59 ++++++++++++++++++++++++++++++++ 1 file changed, 59 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fcasin.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcasin.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcasin.html b/devdocs/c/numeric%2Fcomplex%2Fcasin.html new file mode 100644 index 00000000..379708be --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcasin.html @@ -0,0 +1,59 @@ +

casinf, casin, casinl

Defined in header <complex.h> 
float complex       casinf( float complex z );
+		 (1) (since C99) 
double complex      casin( double complex z );
+		 (2) (since C99) 
long double complex casinl( long double complex z );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define asin( z )
+		 (4) (since C99)
+1-3) Computes the complex arc sine of z with branch cuts outside the interval [−1,+1] along the real axis.
+4) Type-generic macro: If z has type long double complex, casinl is called. if z has type double complex, casin is called, if z has type float complex, casinf is called. If z is real or integer, then the macro invokes the corresponding real function (asinf, asin, asinl). If z is imaginary, then the macro invokes the corresponding real version of the function asinh, implementing the formula \(\small \arcsin({\rm i}y) = {\rm i}{\rm arsinh}(y)\)arcsin(iy) = i arsinh(y), and the return type of the macro is imaginary.

Parameters

+ +
z - complex argument

Return value

If no errors occur, complex arc sine of z is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2; +π/2] along the real axis.

+

Errors and special cases are handled as if the operation is implemented by -I * casinh(I*z)

+

Notes

Inverse sine (or arc sine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.

+

The mathematical definition of the principal value of arc sine is \(\small \arcsin z = -{\rm i}\ln({\rm i}z+\sqrt{1-z^2})\)arcsin z = -iln(iz + √1-z2) For any z, \(\small{ \arcsin(z) = \arccos(-z) - \frac{\pi}{2} }\)arcsin(z) = acos(-z) -

+π/2

Example

#include <stdio.h>
+#include <math.h>
+#include <complex.h>
+ 
+int main(void)
+{
+    double complex z = casin(-2);
+    printf("casin(-2+0i) = %f%+fi\n", creal(z), cimag(z));
+ 
+    double complex z2 = casin(conj(-2)); // or CMPLX(-2, -0.0)
+    printf("casin(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
+ 
+    // for any z, asin(z) = acos(-z) - pi/2
+    double pi = acos(-1);
+    double complex z3 = csin(cacos(conj(-2))-pi/2);
+    printf("csin(cacos(-2-0i)-pi/2) = %f%+fi\n", creal(z3), cimag(z3));
+}

Output:

+
casin(-2+0i) = -1.570796+1.316958i
+casin(-2-0i) (the other side of the cut) = -1.570796-1.316958i
+csin(cacos(-2-0i)-pi/2) = 2.000000+0.000000i

References

See also

+ + + + +
+
(C99)(C99)(C99)
 computes the complex arc cosine
(function)
+
(C99)(C99)(C99)
 computes the complex arc tangent
(function)
+
(C99)(C99)(C99)
 computes the complex sine
(function)
+
(C99)(C99)
 computes arc sine (\({\small\arcsin{x} }\)arcsin(x))
(function)
C++ documentation for asin
+

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

+
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