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94 lines
3.0 KiB
Plaintext
94 lines
3.0 KiB
Plaintext
NAME
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asec - inverse trigonometric secant
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SYNOPSIS
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asec(x [,eps])
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TYPES
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x number (real or complex)
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eps 0 < real < 1, defaults to epsilon()
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return real
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DESCRIPTION
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Returns the inverse trigonometric secant of x to a multiple of eps with error less in
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absolute value than .75 * eps.
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This function is sometimes called arcsec.
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EXAMPLE
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; print asec(0), asec(0.5), asec(1)
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Error E_ASEC_3 1.31695789692481670863i 0
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; print asec(-0.5), asec(-1)
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3.14159265358979323846-1.31695789692481670863i 3.14159265358979323846
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; print asec(.5, 1e-5), asec(.5, 1e-10), asec(.5, 1e-15), asec(.5, 1e-20)
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1.31695i 1.316957897i 1.316957896924816i 1.31695789692481670863i
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; print asec(5), asec(5i)
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1.36943840600456582778 1.57079632679489661923+0.19869011034924140647i
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; print asec(5+5i)
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1.4711326239351014592+0.10033029811220500594i
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; pi = pi(1e-20)
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; print asec(pi/6), asec(pi/3)
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1.26327680856656556836i 0.30137360974529145454
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; print asec(4*pi/3)
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1.32973601406082299099
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qasec(NUMBER *x, NUMBER *eps)
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COMPLEX *c_asec(COMPLEX *c, NUMBER *epsilon)
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SEE ALSO
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sin, cos, tan, cot, sec, csc
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asin, acos, atan, acot, acsc
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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, havercos, hacovercos
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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For general information on trigonometric functions, see:
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https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
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https://en.wikipedia.org/wiki/Versine
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https://en.wikipedia.org/wiki/Exsecant
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https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
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https://en.wikipedia.org/wiki/Chord_(geometry)
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https://en.wikipedia.org/wiki/Secant_line
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https://en.wikipedia.org/wiki/Hartley_transform#cas
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https://en.wikipedia.org/wiki/Cis_(mathematics)
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## Copyright (C) 1999,2021,2023 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 1995/11/13 03:49:00
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## File existed as early as: 1995
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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