sin
Returns the sine of a complex number.
template<class Type>
complex<Type> sin(
const complex<Type>& _ComplexNum
);
Parameters
- _ComplexNum
The complex number whose sine is being determined.
Return Value
The complex number that is the sine of the input complex number.
Remarks
Identities defining the complex sines:
sin (z) = (1/2i)*( exp (iz) – exp (-iz) )
sin (z) = sin (a + bi) = sin (a) cosh (b) + icos (a) sinh (b)
Example
// complex_sin.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>
int main( )
{
using namespace std;
double pi = 3.14159265359;
complex <double> c1 ( 3.0 , 4.0 );
cout << "Complex number c1 = " << c1 << endl;
// Values of sine of a complex number c1
complex <double> c2 = sin ( c1 );
cout << "Complex number c2 = sin ( c1 ) = " << c2 << endl;
double absc2 = abs ( c2 );
double argc2 = arg ( c2 );
cout << "The modulus of c2 is: " << absc2 << endl;
cout << "The argument of c2 is: "<< argc2 << " radians, which is "
<< argc2 * 180 / pi << " degrees." << endl << endl;
// sines of the standard angles in the first
// two quadrants of the complex plane
vector <complex <double> > v1;
vector <complex <double> >::iterator Iter1;
complex <double> vc1 ( polar ( 1.0, pi / 6 ) );
v1.push_back( sin ( vc1 ) );
complex <double> vc2 ( polar ( 1.0, pi / 3 ) );
v1.push_back( sin ( vc2 ) );
complex <double> vc3 ( polar ( 1.0, pi / 2 ) );
v1.push_back( sin ( vc3 ) );
complex <double> vc4 ( polar ( 1.0, 2 * pi / 3 ) );
v1.push_back( sin ( vc4 ) );
complex <double> vc5 ( polar ( 1.0, 5 * pi / 6 ) );
v1.push_back( sin ( vc5 ) );
complex <double> vc6 ( polar ( 1.0, pi ) );
v1.push_back( sin ( vc6 ) );
cout << "The complex components sin (vci), where abs (vci) = 1"
<< "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
cout << *Iter1 << endl;
}
Complex number c1 = (3,4) Complex number c2 = sin ( c1 ) = (3.85374,-27.0168) The modulus of c2 is: 27.2903 The argument of c2 is: -1.42911 radians, which is -81.882 degrees. The complex components sin (vci), where abs (vci) = 1 & arg (vci) = i * pi / 6 of the vector v1 are: (0.85898,0.337596) (0.670731,0.858637) (-1.59572e-013,1.1752) (-0.670731,0.858637) (-0.85898,0.337596) (-0.841471,-1.11747e-013)
Requirements
Header: <complex>
Namespace: std