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# std::sin(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > complex<T> sin( const complex<T>& z ); |  |

Computes complex sine of a complex value `z`.

### [edit] Parameters

z | - | complex value

### [edit] 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.

### [edit] 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

### [edit] 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)

### [edit] See also

cos(std::complex) | computes cosine of a complex number (cos(z)) (function template) [edit]
tan(std::complex) | computes tangent of a complex number (tan(z)) (function template) [edit]
asin(std::complex) (C++11) | computes arc sine of a complex number (arcsin(z)) (function template) [edit]
sin | computes sine (sin(x)) (function) [edit]
sin(std::valarray) | applies the function std::sin to each element of valarray (function template) [edit]
C documentation for csin

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