| Types and the imaginary constant | |||||||||||||||||||||||||||||||
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| Manipulation | |||||||||||||||||||||||||||||||
| Power and exponential functions | |||||||||||||||||||||||||||||||
| Trigonometric functions | |||||||||||||||||||||||||||||||
| Hyperbolic functions | |||||||||||||||||||||||||||||||
Defined in header <complex.h> | ||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (3) | (since C99) | |
Defined in header <tgmath.h> | ||
#define tan( z ) | (4) | (since C99) |
z.z has typelongdoublecomplex,ctanl is called. ifz has typedoublecomplex,ctan is called, ifz has typefloatcomplex,ctanf is called. Ifz is real or integer, then the macro invokes the corresponding real function (tanf,tan,tanl). Ifz is imaginary, then the macro invokes the corresponding real version of the functiontanh, implementing the formulatan(iy) = i tanh(y), and the return type is imaginary.Contents |
| z | - | complex argument |
If no errors occur, the complex tangent ofz is returned.
Errors and special cases are handled as if the operation is implemented by-i*ctanh(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 <stdio.h>#include <math.h>#include <complex.h> int main(void){doublecomplex z= ctan(1);// behaves like real tangent along the real lineprintf("tan(1+0i) = %f%+fi ( tan(1)=%f)\n",creal(z),cimag(z),tan(1)); doublecomplex z2= ctan(I);// behaves like tanh along the imaginary lineprintf("tan(0+1i) = %f%+fi (tanh(1)=%f)\n",creal(z2),cimag(z2),tanh(1));}
Output:
tan(1+0i) = 1.557408+0.000000i ( tan(1)=1.557408)tan(0+1i) = 0.000000+0.761594i (tanh(1)=0.761594)
(C99)(C99)(C99) | computes the complex hyperbolic tangent (function)[edit] |
(C99)(C99)(C99) | computes the complex sine (function)[edit] |
(C99)(C99)(C99) | computes the complex cosine (function)[edit] |
(C99)(C99)(C99) | computes the complex arc tangent (function)[edit] |
(C99)(C99) | computes tangent (\({\small\tan{x} }\)tan(x)) (function)[edit] |
C++ documentation fortan | |
