std::sin(std::complex)

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

#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)

See also

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

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