1.\" $OpenBSD: ctan.3,v 1.2 2013/06/05 03:40:26 tedu Exp $ 2.\" 3.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org> 4.\" 5.\" Permission to use, copy, modify, and distribute this software for any 6.\" purpose with or without fee is hereby granted, provided that the above 7.\" copyright notice and this permission notice appear in all copies. 8.\" 9.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16.\" 17.Dd $Mdocdate: June 5 2013 $ 18.Dt CTAN 3 19.Os 20.Sh NAME 21.Nm ctan , 22.Nm ctanf , 23.Nm ctanl 24.Nd complex circular tangent 25.Sh SYNOPSIS 26.In complex.h 27.Ft double complex 28.Fn ctan "double complex z" 29.Ft float complex 30.Fn ctanf "float complex z" 31.Ft long double complex 32.Fn ctanl "long double complex z" 33.Sh DESCRIPTION 34The 35.Fn ctan , 36.Fn ctanf 37and 38.Fn ctanl 39functions compute the complex circular tangent of 40.Fa z . 41.Pp 42If 43.Fa z 44= x + iy, then 45.Bd -literal -offset indent 46ctan(z) = (sin(2x) + i sinh(2y)) / (cos(2x) + cosh(2y)). 47.Ed 48.Pp 49On the real axis the denominator is zero at odd multiples of Pi/2. 50The denominator is evaluated by its Taylor series near these points. 51.Bd -literal -offset indent 52ctan(z) = -i ctanh(iz). 53.Ed 54.Sh RETURN VALUES 55The 56.Fn ctan , 57.Fn ctanf 58and 59.Fn ctanl 60functions return the complex circular tangent of 61.Fa z . 62.Sh SEE ALSO 63.Xr ccos 3 , 64.Xr csin 3 65.Sh STANDARDS 66The 67.Fn ctan , 68.Fn ctanf 69and 70.Fn ctanl 71functions conform to 72.St -isoC-99 . 73