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%2Fcacos.html | 76 ++++++++++++++++++++++++++++++++ 1 file changed, 76 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fcacos.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcacos.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcacos.html b/devdocs/c/numeric%2Fcomplex%2Fcacos.html new file mode 100644 index 00000000..d5f7cc0a --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcacos.html @@ -0,0 +1,76 @@ +

cacosf, cacos, cacosl

Defined in header <complex.h> 
float complex       cacosf( float complex z );
+		 (1) (since C99) 
double complex      cacos( double complex z );
+		 (2) (since C99) 
long double complex cacosl( long double complex z );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define acos( z )
+		 (4) (since C99)
+1-3) Computes the complex arc cosine 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, cacosl is called. if z has type double complex, cacos is called, if z has type float complex, cacosf is called. If z is real or integer, then the macro invokes the corresponding real function (acosf, acos, acosl). If z is imaginary, then the macro invokes the corresponding complex number version.

Parameters

+ +
z - complex argument

Return value

If no errors occur, complex arc cosine of z is returned, in the range a strip unbounded along the imaginary axis and in the interval [0; π] along the real axis.

+

Error handling and special values

Errors are reported consistent with math_errhandling.

+

If the implementation supports IEEE floating-point arithmetic,

+

Notes

Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventially placed at the line segments (-∞,-1) and (1,∞) of the real axis. The mathematical definition of the principal value of arc cosine is acos z =

+1/2π + iln(iz + √1-z2)

For any z, acos(z) = π - acos(-z)

+

Example

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

Output:

+
cacos(-2+0i) = 3.141593-1.316958i
+cacos(-2-0i) (the other side of the cut) = 3.141593+1.316958i
+ccos(pi - cacos(-2-0i) = 2.000000+0.000000i

References

See also

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

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

+
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