.\"	$OpenBSD: ctan.3,v 1.2 2013/06/05 03:40:26 tedu Exp $
.\"
.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
.\"
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.Dd $Mdocdate: June 5 2013 $
.Dt CTAN 3
.Os
.Sh NAME
.Nm ctan ,
.Nm ctanf ,
.Nm ctanl
.Nd complex circular tangent
.Sh SYNOPSIS
.In 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 .