.\"	$OpenBSD: ctan.3,v 1.1 2011/07/20 17:50:43 martynas Exp $
.\"
.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
.\"
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.Dd $Mdocdate: July 20 2011 $
.Dt CTAN 3
.Os
.Sh NAME
.Nm ctan ,
.Nm ctanf ,
.Nm ctanl
.Nd complex circular tangent
.Sh SYNOPSIS
.Fd #include <complex.h>
.Ft double complex
.Fn ctan "double complex z"
.Ft float complex
.Fn ctanf "float complex z"
.Ft long double complex
.Fn ctanl "long double complex z"
.Sh DESCRIPTION
The
.Fn ctan ,
.Fn ctanf
and
.Fn ctanl
functions compute the complex circular tangent of
.Fa z .
.Pp
If
.Fa z
= x + iy, then
.Bd -literal -offset indent
ctan(z) = (sin(2x) + i sinh(2y)) / (cos(2x) + cosh(2y)).
.Ed
.Pp
On the real axis the denominator is zero at odd multiples of Pi/2.
The denominator is evaluated by its Taylor series near these points.
.Bd -literal -offset indent
ctan(z) = -i ctanh(iz).
.Ed
.Sh RETURN VALUES
The
.Fn ctan ,
.Fn ctanf
and
.Fn ctanl
functions return the complex circular tangent of
.Fa z .
.Sh SEE ALSO
.Xr ccos 3 ,
.Xr csin 3
.Sh STANDARDS
The
.Fn ctan ,
.Fn ctanf
and
.Fn ctanl
functions conform to
.St -isoC-99 .