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Defined in header <complex> | ||
template<class T> complex<T> tan(const complex<T>& z); | ||
Computes complex tangent of a complex valuez.
Contents |
| z | - | complex value |
If no errors occur, the complex tangent ofz is returned.
Errors and special cases are handled as if the operation is implemented by-i* std::tanh(i* z), wherei is the imaginary unit.
Tangent is an analytical function on the complex plain and has no branch cuts. It is periodic with respect to the real component, with period πi, and has poles of the first order along the real line, at coordinates(π(1/2 + n), 0). However no common floating-point representation is able to represent π/2 exactly, thus there is no value of the argument for which a pole error occurs.
Mathematical definition of the tangent istan z =| i(e-iz -eiz ) |
| e-iz +eiz |
#include <cmath>#include <complex>#include <iostream> int main(){std::cout<<std::fixed;std::complex<double> z(1.0,0.0);// behaves like real tangent along the real linestd::cout<<"tan"<< z<<" = "<<std::tan(z)<<" ( tan(1) = "<<std::tan(1)<<")\n"; std::complex<double> z2(0.0,1.0);// behaves like tanh along the imaginary linestd::cout<<"tan"<< z2<<" = "<<std::tan(z2)<<" (tanh(1) = "<<std::tanh(1)<<")\n";}
Output:
tan(1.000000,0.000000) = (1.557408,0.000000) ( tan(1) = 1.557408)tan(0.000000,1.000000) = (0.000000,0.761594) (tanh(1) = 0.761594)
| computes sine of a complex number (\({\small\sin{z}}\)sin(z)) (function template)[edit] | |
| computes cosine of a complex number (\({\small\cos{z}}\)cos(z)) (function template)[edit] | |
(C++11) | computes arc tangent of a complex number (\({\small\arctan{z}}\)arctan(z)) (function template)[edit] |
(C++11)(C++11) | computes tangent (\({\small\tan{x}}\)tan(x)) (function)[edit] |
| applies the functionstd::tan to each element of valarray (function template)[edit] | |
C documentation forctan | |
