NAME
    sec - trigonometric secant

SYNOPSIS
    sec(x [,eps])

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

    return	real

DESCRIPTION
    Calculate the secant of x to a multiple of eps, with error less
    in absolute value than .75 * eps.

    This function is equivalent to:

	sec(x) = 1 / cos(x)

EXAMPLE
    ; print sec(1, 1e-5), sec(1, 1e-10), sec(1, 1e-15), sec(1, 1e-20)
    1.85082 1.8508157177 1.850815717680926 1.85081571768092561791

    ; print sec(2 + 3i, 1e-5), sec(2 + 3i, 1e-10)
    ~-0.04167497639869547021+~0.09061109101765280898i ~-0.04167496441100888150+~0.09061113719571288336i

    ; pi = pi(1e-20)
    ; print 1e-10), sec(pi/6, 1e-10), sec(pi/3, 1e-10), sec(pi, 1e-10)
    1.1547005384 2 -1

    ; print sec(1/2), sec(5/7), sec(42/7)
    1.13949392732454912231 1.3235192673191814545 1.04148192659510767648

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qsec(NUMBER *x, NUMBER *eps)
    COMPLEX *c_sec(COMPLEX *c, NUMBER *eps)

SEE ALSO
    sin, cos, tan, cot, csc
    asin, acos, atan, acot, asec, acsc
    versin, coversin, vercos, avercos
    aversin, acoversin, covercos, acovercos
    epsilon

## Copyright (C) 1999,2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## 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
## distributed with calc under the filename COPYING-LGPL.  You should have
## 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:	1995/11/13 03:49:00
## File existed as early as:	1995
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/