Std::sin(std::complex) (3) Linux Manual Page

std::sin(std::complex) – std::sin(std::complex)

Synopsis

Defined in header<complex>

    template <class T>

    complex<T> sin(const complex<T> &z);

Computes complex sine of a complex value z.

Parameters

z – complex value

Return value

If no errors occur, the complex sine of z is returned.
Errors and special cases are handled as if the operation is implemented by -i * std::sinh(i*z), where i is the imaginary unit.

Notes

The sine is an entire function on the complex plane, and has no branch cuts.
Mathematical definition of the sine is sin z =
eiz
-e-iz
2i

Example

// Run this code

#include <iostream>

#include <cmath>

#include <complex>
int main()

{
    std::cout << std::fixed;
    std::complex<double> z(1, 0); // behaves like real sine along the real line
    std::cout << "sin" << z << " = " << std::sin(z)
              << " ( sin(1) = " << std::sin(1) << ")\n";
    std::complex<double> z2(0, 1); // behaves like sinh along the imaginary line
    std::cout << "sin" << z2 << " = " << std::sin(z2)
              << " (sinh(1) = " << std::sinh(1) << ")\n";
}

Output:

sin(1.000000,0.000000) = (0.841471,0.000000) ( sin(1) = 0.841471)
sin(0.000000,1.000000) = (0.000000,1.175201) (sinh(1) = 1.175201)

                   computes cosine of a complex number (cos(z))
cos(std::complex) (function template)
                   computes tangent of a complex number (tan(z))
tan(std::complex) (function template)
asin(std::complex) computes arc sine of a complex number (arcsin(z))
                   (function template)
(C++11)
sin
sinf
sinl computes sine (sin(x))
                   (function)
(C++11)
(C++11)
                   applies the function std::sin to each element of valarray
sin(std::valarray) (function template)

std::sin(std::complex) (3) Linux Manual Page