NAME
    atan - inverse trigonometric tangent

SYNOPSIS
    atan(x [,eps])

TYPES
    x		number (real or complex)
    eps		0 < real < 1, defaults to epsilon()

    return	real

DESCRIPTION
    Returns the inverse trigonometric tangent of x to a multiple of eps with error less in
    absolute value than .75 * eps.

    This function is sometimes called arctan.

EXAMPLE
    ; print atan(0), atan(0.5), atan(1)
    0 0.46364760900080611621 0.78539816339744830962

    ; print atan(-0.5), atan(-1)
    -0.46364760900080611621 -0.78539816339744830962

    ; print atan(.5, 1e-5), atan(.5, 1e-10), atan(.5, 1e-15), atan(.5, 1e-20)
    0.46365 0.463647609 0.463647609000806 0.46364760900080611621

    ; print atan(5), atan(5i)
    1.37340076694501586086 1.57079632679489661923+0.20273255405408219099i

    ; print atan(5+5i)
    ~1.47013777260757623920+0.09932544936725086122i

    ; pi = pi(1e-20)
    ; print atan(pi/6), atan(pi/3)
    0.48234790710102497548 0.80844879263002203131

    ; print atan(4*pi/3)
    1.33645023930656045846

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qatan(NUMBER *x, NUMBER *eps)
    COMPLEX *c_atan(COMPLEX *c, NUMBER *epsilon)

SEE ALSO
    sin, cos, tan, cot, sec, csc
    asin, acos, acot, asec, acsc
    versin, coversin, vercos, covercos
    aversin, acoversin, avercos, acovercos
    haversin, hacoversin, havercos, hacovercos
    ahaversin, hacoversin, havercos, ahacovercos
    epsilon

## Copyright (C) 1999,2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
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## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:	1994/03/19 01:40:25
## File existed as early as:	1994
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/