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Defined in header <complex> | ||
template<class T> std::complex<T> asin(conststd::complex<T>& z); | (since C++11) | |
Computes complex arc sine of a complex valuez. Branch cut exists outside the interval[−1, +1] along the real axis.
Contents |
| z | - | complex value |
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 *std::asinh(i * z), wherei is the imaginary unit.
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 <cmath>#include <complex>#include <iostream> int main(){std::cout<<std::fixed;std::complex<double> z1(-2.0,0.0);std::cout<<"asin"<< z1<<" = "<<std::asin(z1)<<'\n'; std::complex<double> z2(-2.0,-0.0);std::cout<<"asin"<< z2<<" (the other side of the cut) = "<<std::asin(z2)<<'\n'; // for any z, asin(z) = acos(−z) − pi / 2constdouble pi=std::acos(-1);std::complex<double> z3=std::acos(z2)- pi/2;std::cout<<"sin(acos"<< z2<<" - pi / 2) = "<<std::sin(z3)<<'\n';}
Output:
asin(-2.000000,0.000000) = (-1.570796,1.316958)asin(-2.000000,-0.000000) (the other side of the cut) = (-1.570796,-1.316958)sin(acos(-2.000000,-0.000000) - pi / 2) = (2.000000,0.000000)
(C++11) | computes arc cosine of a complex number (\({\small\arccos{z}}\)arccos(z)) (function template)[edit] |
(C++11) | computes arc tangent of a complex number (\({\small\arctan{z}}\)arctan(z)) (function template)[edit] |
| computes sine of a complex number (\({\small\sin{z}}\)sin(z)) (function template)[edit] | |
(C++11)(C++11) | computes arc sine (\({\small\arcsin{x}}\)arcsin(x)) (function)[edit] |
| applies the functionstd::asin to each element of valarray (function template)[edit] | |
C documentation forcasin | |
