std::sin(std::complex)

 

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20)   operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

 

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

Run this code

#include <cmath>
#include <complex>
#include <iostream>
 
int main()
{
    std::cout << std::fixed;
    std::complex<double> z(1.0, 0.0); // 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(0.0, 1.0); // 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

cos(std::complex)	computes cosine of a complex number (\({\small\cos{z} }\)cos(z)) (function template)
tan(std::complex)	computes tangent of a complex number (\({\small\tan{z} }\)tan(z)) (function template)
asin(std::complex) (C++11)	computes arc sine of a complex number (\({\small\arcsin{z} }\)arcsin(z)) (function template)
sinsinfsinl (C++11)(C++11)	computes sine (\({\small\sin{x} }\)sin(x)) (function)
sin(std::valarray)	applies the function std::sin to each element of valarray (function template)