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93 lines
3.0 KiB
Plaintext
93 lines
3.0 KiB
Plaintext
NAME
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cis - Euler's formula
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SYNOPSIS
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cis(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 Euler's formula value 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 cosine and sine, is equivalent to:
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cis(x) = cos(x) + 1i*sin(x)
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cis(x) = exp(1i * x)
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EXAMPLE
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; print cis(1/2), cis(5/7)
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0.87758256189037271612+0.47942553860420300027i 0.75556134670069659847+0.6550778971785185742i
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; print cis(42/7)
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0.96017028665036602055-0.27941549819892587281i
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; print cis(1, 1e-5), cis(1, 1e-10), cis(1, 1e-15)
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0.5403+0.84147i 0.5403023059+0.8414709848i 0.54030230586814+0.841470984807896i
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; print cis(1, 1e-20)
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0.5403023058681397174+0.84147098480789650665i
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; print cis(2 + 3i, 1e-5), cis(2 + 3i, 1e-10)
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-0.02072+0.04527i -0.020718731+0.0452712531i
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; pi = pi(1e-20)
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; print cis(pi/6), cis(pi/2), cis(pi)
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0.86602540378443864676+0.5i 1i -1
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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COMPLEX *c_cis(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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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, 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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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 23:11:18
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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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