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2c4abcd2b7
Added the following new trigonometric functions:
cas(x [,eps]) trigonometric cosine plus sine
cis(x [,eps]) Euler's formula
90 lines
3.0 KiB
Plaintext
90 lines
3.0 KiB
Plaintext
NAME
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acrd - inverse trigonometric chord of a unit circle
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SYNOPSIS
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acrd(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 number
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DESCRIPTION
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Calculate angle of unit circle chord of length x to a multiple of eps with error less in
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absolute value than .75 * eps.
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A chord of a circle is a straight line segment whose endpoints lie on a arc of a circle.
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A chord extended infinitely on both directions into a line would produce a secant line.
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This function is sometimes called chord, is equivalent to:
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acrd(x) = 2 * asin(x / 2)
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EXAMPLE
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; print acrd(1/2), acrd(5/7), acrd(42/7)
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0.50536051028415730696 0.73041444258073348124 3.14159265358979323846-3.52549434807817210092i
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; print acrd(1, 1e-5), acrd(1, 1e-10), acrd(1, 1e-15), acrd(1, 1e-20)
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1.0472 1.0471975512 1.047197551196598 1.04719755119659774616
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; print acrd(2 + 3i, 1e-5), acrd(2 + 3i, 1e-10)
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1.0472+2.63392i 1.0471975512+2.6339157938i
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; pi = pi(1e-20)
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; print acrd(pi/6), acrd(pi/2), acrd(pi)
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0.52977229404847186194 1.80667822153302569472 3.14159265358979323846-2.04645495709510115864i
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qacrd(NUMBER *x, NUMBER *eps)
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COMPLEX *c_acrd(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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sin, cos, tan, cot, sec, csc
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asin, acos, atan, acot, asec, acsc
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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
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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) 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: 2023/10/02 16:49:42
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## File existed as early as: 2023
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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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