ctanf, ctan, ctanl
From cppreference.com
| Defined in header <complex.h>
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| (1) | (since 哋它亢99) | |
| (2) | (since 哋它亢99) | |
| (3) | (since 哋它亢99) | |
| Defined in header <tgmath.h>
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| #define tan( z ) |
(4) | (since 哋它亢99) |
1-3) Computes the complex tangent of
z.4) 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.Parameters
| z | - | complex argument |
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 =| i(e-iz -eiz ) |
| e-iz +eiz |
Example
Run this code
#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)
References
- 哋它亢11 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)
- 哋它亢99 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
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes the complex hyperbolic tangent (function) |
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes the complex sine (function) |
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes the complex cosine (function) |
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes the complex arc tangent (function) |
| (哋它亢99)(哋它亢99) |
computes tangent (tan(x)) (function) |