sinh

Visual Studio 2013

Returns the hyperbolic sine of a complex number.

```template<class Type>
complex<Type> sinh(
const complex<Type>& _ComplexNum
);
```

Parameters

_ComplexNum

The complex number whose hyperbolic sine is being determined.

Return Value

The complex number that is the hyperbolic sine of the input complex number.

Remarks

Identities defining the complex hyperbolic sines:

sinh (z) = (1/2)*( exp (z) – exp (-z) )

sinh (z) = sinh (a + bi) = sinh (a) cos (b) + icosh (a) sin (b)

Example

```// complex_sinh.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 = sinh ( c1 );
cout << "Complex number c2 = sinh ( 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;

// Hyperbolic 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( sinh ( vc1 ) );
complex <double> vc2  ( polar ( 1.0, pi / 3 ) );
v1.push_back( sinh ( vc2 ) );
complex <double> vc3  ( polar ( 1.0, pi / 2 ) );
v1.push_back( sinh ( vc3) );
complex <double> vc4  ( polar ( 1.0, 2 * pi / 3 ) );
v1.push_back( sinh ( vc4 ) );
complex <double> vc5  ( polar ( 1.0, 5 * pi / 6 ) );
v1.push_back( sinh ( vc5 ) );
complex <double> vc6  ( polar ( 1.0, pi ) );
v1.push_back( sinh ( vc6 ) );

cout << "The complex components sinh (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 = sinh ( c1 ) = (-6.54812,-7.61923)
The modulus of c2 is: 10.0464
The argument of c2 is: -2.28073 radians, which is -130.676 degrees.

The complex components sinh (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0.858637,0.670731)
(0.337596,0.85898)
(-5.58735e-014,0.841471)
(-0.337596,0.85898)
(-0.858637,0.670731)
(-1.1752,-3.19145e-013)```