| Types and the imaginary constant | |||||||||||||||||||||||||||||||
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| Manipulation | |||||||||||||||||||||||||||||||
| Power and exponential functions | |||||||||||||||||||||||||||||||
| Trigonometric functions | |||||||||||||||||||||||||||||||
| Hyperbolic functions | |||||||||||||||||||||||||||||||
Defined in header <complex.h> | ||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (3) | (since C99) | |
Defined in header <tgmath.h> | ||
#define asin( z ) | (4) | (since C99) |
z with branch cuts outside the interval[−1,+1] along the real axis.z has typelongdoublecomplex,casinl is called. ifz has typedoublecomplex,casin is called, ifz has typefloatcomplex,casinf is called. Ifz is real or integer, then the macro invokes the corresponding real function (asinf,asin,asinl). Ifz is imaginary, then the macro invokes the corresponding real version of the functionasinh, 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.Contents |
| z | - | complex argument |
If no errors occur, complex arc sine ofz 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)
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
)
| π |
| 2 |
#include <stdio.h>#include <math.h>#include <complex.h> int main(void){doublecomplex z= casin(-2);printf("casin(-2+0i) = %f%+fi\n",creal(z),cimag(z)); doublecomplex 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/2double pi=acos(-1);doublecomplex 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+1.316958icasin(-2-0i) (the other side of the cut) = -1.570796-1.316958icsin(cacos(-2-0i)-pi/2) = 2.000000+0.000000i
(C99)(C99)(C99) | computes the complex arc cosine (function)[edit] |
(C99)(C99)(C99) | computes the complex arc tangent (function)[edit] |
(C99)(C99)(C99) | computes the complex sine (function)[edit] |
(C99)(C99) | computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)[edit] |
C++ documentation forasin | |
