#define tan( z )
(4) (since C99)1-3) Computes the complex tangent of z.
Type-generic macro: If
z
has type
long double complex,
ctanl
is called. if
z
has type
double complex,
ctan
is called, if
z
has type
float complex,
ctanf
is called. If
z
is real or integer, then the macro invokes the corresponding real function (
tanf,
tan,
tanl). If
z
is imaginary, then the macro invokes the corresponding real version of the function
tanh, implementing the formula
tan(iy) = i tanh(y), and the return type is imaginary.
[edit] Parameters [edit] Return valueIf no errors occur, the complex tangent of z is returned.
Errors and special cases are handled as if the operation is implemented by -i * ctanh(i*z), where i 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 (Ï(1/2 + n), 0). However no common floating-point representation is able to represent Ï/2 exactly, thus there is no value of the argument for which a pole error occurs.
Mathematical definition of the tangent is
tan z = [edit] Example#include <stdio.h>
#include <math.h>
#include <complex.h>
int main(void)
{
double complex z = ctan(1); // behaves like real tangent along the real line
printf("tan(1+0i) = %f%+fi ( tan(1)=%f)\n", creal(z), cimag(z), tan(1));
double complex z2 = ctan(I); // behaves like tanh along the imaginary line
printf("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)[edit] References
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