# std::sin(std::complex) (3) - Linux Man Pages

## NAME

std::sin(std::complex) - std::sin(std::complex)

## Synopsis

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)