| 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) |
| computes sine (sin(x)) (function) | |
applies the function std::sin to each element of valarray (function template) | |
C documentation for csin | |
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