NAME¶

std::cos(std::complex) - std::cos(std::complex)

Synopsis¶

Defined in header <complex>
template< class T >
complex<T> cos( const complex<T>& z );

Computes complex cosine of a complex value z.

Parameters¶

z - complex value

Return value¶

If no errors occur, the complex cosine of z is returned.

Errors and special cases are handled as if the operation is implemented by
std::cosh(i*z), where i is the imaginary unit.

Notes¶

The cosine is an entire function on the complex plane, and has no branch cuts.

Mathematical definition of the cosine is cos z =

eiz
+e-iz
2

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 cosine along the real line
std::cout << "cos" << z << " = " << std::cos(z)
<< " ( cos(1) = " << std::cos(1) << ")\n";

std::complex<double> z2(0, 1); // behaves like real cosh along the imaginary line
std::cout << "cos" << z2 << " = " << std::cos(z2)
<< " (cosh(1) = " << std::cosh(1) << ")\n";
}

Output:¶

cos(1.000000,0.000000) = (0.540302,-0.000000) ( cos(1) = 0.540302)
cos(0.000000,1.000000) = (1.543081,-0.000000) (cosh(1) = 1.543081)

See also¶

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