ctanf

float complex       ctanf( float complex z );

double complex      ctan( double complex z );

long double complex ctanl( long double complex z );

#define tan( z )

Parameters

Return value

If 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.

Notes

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 is tan z =

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));
}

tan(1+0i) = 1.557408+0.000000i ( tan(1)=1.557408)
tan(0+1i) = 0.000000+0.761594i (tanh(1)=0.761594)

References

• C11 standard (ISO/IEC 9899:2011):
  • 7.3.5.6 The ctan functions (p: 192)
  • 7.25 Type-generic complex <tgmath.h> (p: 373-375)
  • G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
  • 7.3.5.6 The ctan functions (p: 174)
  • 7.22 Type-generic complex <tgcomplex.h> (p: 335-337)
  • G.7 Type-generic math <tgmath.h> (p: 480)

See also