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88 lines
3.0 KiB
Plaintext
88 lines
3.0 KiB
Plaintext
NAME
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havercos - half versed trigonometric cosine
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SYNOPSIS
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havercos(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 the half versed trigonometric cosine 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 haverc, or haverconsine, is equivalent to:
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havercos(x) = vercos(x) / 2
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havercos(x) = (1 + cos(x)) / 2
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EXAMPLE
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; print havercos(1/2), havercos(5/7), havercos(42/7)
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0.93879128094518635806 ~0.87778067335034829924 ~0.98008514332518301028
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; print havercos(1, 1e-5), havercos(1, 1e-10), havercos(1, 1e-15), havercos(1, 1e-20)
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0.77015 0.77015115295 0.77015115293407 0.7701511529340698587
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; print havercos(2 + 3i, 1e-5), havercos(2 + 3i, 1e-10)
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-1.594815-4.554615i -1.5948128455-4.5546139469i
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; pi = pi(1e-20)
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; print havercos(pi/6), havercos(pi/2), havercos(pi)
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0.93301270189221932338 0.5 0
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qhavercos(NUMBER *x, NUMBER *eps)
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COMPLEX *c_havercos(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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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, 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) 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: 2023/09/24 11:13:28
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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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