Difference between revisions of "cpp/numeric/complex/cos"
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{{cpp/title|cos{{small|(std::complex)}}}} | {{cpp/title|cos{{small|(std::complex)}}}} | ||
{{cpp/numeric/complex/navbar}} | {{cpp/numeric/complex/navbar}} | ||
| − | {{ddcl | header=complex | 1= | + | {{ddcl|header=complex|1= |
template< class T > | template< class T > | ||
complex<T> cos( const complex<T>& z ); | complex<T> cos( const complex<T>& z ); | ||
}} | }} | ||
| − | Computes complex cosine of a complex value {{ | + | Computes complex cosine of a complex value {{c|z}}. |
===Parameters=== | ===Parameters=== | ||
{{par begin}} | {{par begin}} | ||
| − | {{par | z | complex value}} | + | {{par|z|complex value}} |
{{par end}} | {{par end}} | ||
===Return value=== | ===Return value=== | ||
| − | If no errors occur, the complex cosine of {{ | + | If no errors occur, the complex cosine of {{c|z}} is returned. |
| − | Errors and special cases are handled as if the operation is implemented by {{ | + | Errors and special cases are handled as if the operation is implemented by {{tt|[[cpp/numeric/complex/cosh|std::cosh]](i * z)}}, where {{tt|i}} is the imaginary unit. |
===Notes=== | ===Notes=== | ||
The cosine is an entire function on the complex plane, and has no branch cuts. | The cosine is an entire function on the complex plane, and has no branch cuts. | ||
| − | Mathematical definition of the cosine is {{math|cos z {{=}} {{mfrac|e{{su|p=iz}}+e{{su|p=-iz}}|2}}}} | + | Mathematical definition of the cosine is {{math|cos z {{=}} {{mfrac|e{{su|p=iz}}+e{{su|p=-iz}}|2}}}}. |
===Example=== | ===Example=== | ||
| − | {{example | + | {{example |
| − | + | |code= | |
| − | + | ||
#include <cmath> | #include <cmath> | ||
#include <complex> | #include <complex> | ||
| + | #include <iostream> | ||
int main() | int main() | ||
{ | { | ||
std::cout << std::fixed; | std::cout << std::fixed; | ||
| − | std::complex<double> z(1, 0); // behaves like real cosine along the real line | + | std::complex<double> z(1.0, 0.0); // behaves like real cosine along the real line |
std::cout << "cos" << z << " = " << std::cos(z) | std::cout << "cos" << z << " = " << std::cos(z) | ||
<< " ( cos(1) = " << std::cos(1) << ")\n"; | << " ( cos(1) = " << std::cos(1) << ")\n"; | ||
| − | std::complex<double> z2(0, 1); // behaves like real cosh along the imaginary line | + | std::complex<double> z2(0.0, 1.0); // behaves like real cosh along the imaginary line |
std::cout << "cos" << z2 << " = " << std::cos(z2) | std::cout << "cos" << z2 << " = " << std::cos(z2) | ||
<< " (cosh(1) = " << std::cosh(1) << ")\n"; | << " (cosh(1) = " << std::cosh(1) << ")\n"; | ||
} | } | ||
| − | + | |output= | |
cos(1.000000,0.000000) = (0.540302,-0.000000) ( cos(1) = 0.540302) | 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) | cos(0.000000,1.000000) = (1.543081,-0.000000) (cosh(1) = 1.543081) | ||
| Line 48: | Line 48: | ||
===See also=== | ===See also=== | ||
{{dsc begin}} | {{dsc begin}} | ||
| − | {{dsc inc | cpp/numeric/complex/dsc sin}} | + | {{dsc inc|cpp/numeric/complex/dsc sin}} |
| − | {{dsc inc | cpp/numeric/complex/dsc tan}} | + | {{dsc inc|cpp/numeric/complex/dsc tan}} |
| − | {{dsc inc | cpp/numeric/complex/dsc acos}} | + | {{dsc inc|cpp/numeric/complex/dsc acos}} |
| − | {{dsc inc | cpp/numeric/math/dsc cos}} | + | {{dsc inc|cpp/numeric/math/dsc cos}} |
| − | {{dsc inc | cpp/numeric/valarray/dsc cos}} | + | {{dsc inc|cpp/numeric/valarray/dsc cos}} |
| − | {{dsc see c | c/numeric/complex/ccos}} | + | {{dsc see c|c/numeric/complex/ccos}} |
{{dsc end}} | {{dsc end}} | ||
| − | + | {{langlinks|de|es|fr|it|ja|pt|ru|zh}} | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
Latest revision as of 23:08, 21 April 2023
| Defined in header <complex>
|
||
| template< class T > complex<T> cos( const complex<T>& z ); |
||
Computes complex cosine of a complex value z.
Contents |
[edit] Parameters
| z | - | complex value |
[edit] 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.
[edit] 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 |
[edit] 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 cosine along the real line std::cout << "cos" << z << " = " << std::cos(z) << " ( cos(1) = " << std::cos(1) << ")\n"; std::complex<double> z2(0.0, 1.0); // 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)
[edit] See also
| computes sine of a complex number (sin(z)) (function template) | |
| computes tangent of a complex number (tan(z)) (function template) | |
| (C++11) |
computes arc cosine of a complex number (arccos(z)) (function template) |
| (C++11)(C++11) |
computes cosine (cos(x)) (function) |
| applies the function std::cos to each element of valarray (function template) | |
| C documentation for ccos
| |
