< cpp‎ | numeric‎ | complex
Defined in header <complex>
template< class T >
complex<T> asin( const complex<T>& z );
(since C++11)

Computes complex arc sine of a complex value z. Branch cut exists outside the interval [−1 ; +1] along the real axis.


[edit] Parameters

z - complex value

[edit] 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 * std::asinh(i*z), where i is the imaginary unit.

[edit] 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 asin z = -iln(iz + 1-z2

For any z, asin(z) = acos(-z) -

[edit] Example

#include <iostream>
#include <cmath>
#include <complex>
int main()
    std::cout << std::fixed;
    std::complex<double> z1(-2, 0);
    std::cout << "acos" << z1 << " = " << std::acos(z1) << '\n';
    std::complex<double> z2(-2, -0.0);
    std::cout << "acos" << z2 << " (the other side of the cut) = "
              << std::acos(z2) << '\n';
    // for any z, acos(z) = pi - acos(-z)
    const double pi = std::acos(-1);
    std::complex<double> z3 = pi - std::acos(z2);
    std::cout << "cos(pi - acos" << z2 << ") = " << std::cos(z3) << '\n';


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)

[edit] See also

computes arc cosine of a complex number (arccos(z))
(function template) [edit]
computes arc tangent of a complex number (arctan(z))
(function template) [edit]
computes sine of a complex number (sin(z))
(function template) [edit]
computes arc sine (arcsin(x))
(function) [edit]
applies the function std::asin to each element of valarray
(function template) [edit]
C documentation for casin