NAME¶

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)

See also¶

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