drygdryg/calc
1
0
Fork 0
mirror of https://github.com/lcn2/calc.git synced 2025-08-16 01:03:29 +03:00
Code Issues Packages Projects Releases Wiki Activity

add trigonometric chord of a unit circle functions

Browse Source 
Improve builtin function strings, as printed by help builtin,
that use an optional accuracy (epsilon) arg by adding a comma.

Added the following new trigonometric functions:

    crd(x [,eps])		trigonometric chord of a unit circle
    acrd(x [,eps])		inverse trigonometric chord of a unit circle
This commit is contained in:
Landon Curt Noll
2023-10-02 22:43:33 -07:00
parent c78a893862
commit 26fc394089
44 changed files with 1246 additions and 118 deletions
Download Patch File Download Diff File Expand all files Collapse all files

88
help/crd Normal file
View File

@@ -0,0 +1,88 @@
NAME
crd - trigonometric chord of a unit circle
SYNOPSIS
crd(x [,eps])
TYPES
x number (real or complex)
eps 0 < real < 1, defaults to epsilon()
return number
DESCRIPTION
Calculate length of unit circle chord with angle x to a multiple of eps with error less in
absolute value than .75 * eps.
A chord of a circle is a straight line segment whose endpoints lie on a arc of a circle.
A chord extended infinitely on both directions into a line would produce a secant line.
This function is sometimes called chord, is equivalent to:
crd(x) = 2 * sin(x / 2)
EXAMPLE
; print crd(1/2), crd(5/7), crd(42/7)
0.4948079185090458592 0.6991976162706840944 0.2822400161197344442
; print crd(1, 1e-5), crd(1, 1e-10), crd(1, 1e-15), crd(1, 1e-20)
0.95886 0.9588510772 0.958851077208406 0.95885107720840600054
; print crd(2 + 3i, 1e-5), crd(2 + 3i, 1e-10)
3.95896+2.3009i 3.9589688712+2.3009091988i
; pi = pi(1e-20)
; print crd(pi/6), crd(pi/2), crd(pi)
0.5176380902050415247 1.4142135623730950488 2
LIMITS
0 < eps < 1
LINK LIBRARY
NUMBER *qcrd(NUMBER *x, NUMBER *eps)
COMPLEX *c_crd(COMPLEX *x, NUMBER *eps)
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
coversin, vercos, covercos
aversin, acoversin, avercos, acovercos
haversin, hacoversin, havercos, hacovercos
ahaversin, hacoversin, havercos, ahacovercos
exsec, aexsec, excsc, aexcsc
acrd
epsilon
EXTERNAL RESOURCES
For general information on trigonometric functions, see:
https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
https://en.wikipedia.org/wiki/Versine
https://en.wikipedia.org/wiki/Exsecant
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
https://en.wikipedia.org/wiki/Chord_(geometry)
https://en.wikipedia.org/wiki/Secant_line
https://en.wikipedia.org/wiki/Hartley_transform#cas
https://en.wikipedia.org/wiki/Cis_(mathematics)
## Copyright (C) 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: 2023/10/02 16:49:42
## File existed as early as: 2023
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/