mirror of
https://github.com/lcn2/calc.git
synced 2025-08-19 01:13:27 +03:00
26fc394089
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
89 lines
3.0 KiB
Plaintext
89 lines
3.0 KiB
Plaintext
NAME
|
|
acrd - inverse trigonometric chord of a unit circle
|
|
|
|
SYNOPSIS
|
|
acrd(x [,eps])
|
|
|
|
TYPES
|
|
x number (real or complex)
|
|
eps 0 < real < 1, defaults to epsilon()
|
|
|
|
return number
|
|
|
|
DESCRIPTION
|
|
Calculate angle of unit circle chord of length 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:
|
|
|
|
acrd(x) = 2 * asin(x / 2)
|
|
|
|
EXAMPLE
|
|
; print acrd(1/2), acrd(5/7), acrd(42/7)
|
|
0.50536051028415730696 0.73041444258073348124 3.14159265358979323846-3.52549434807817210092i
|
|
|
|
; print acrd(1, 1e-5), acrd(1, 1e-10), acrd(1, 1e-15), acrd(1, 1e-20)
|
|
1.0472 1.0471975512 1.047197551196598 1.04719755119659774616
|
|
|
|
; print acrd(2 + 3i, 1e-5), acrd(2 + 3i, 1e-10)
|
|
1.0472+2.63392i 1.0471975512+2.6339157938i
|
|
|
|
; pi = pi(1e-20)
|
|
; print acrd(pi/6), acrd(pi/2), acrd(pi)
|
|
0.52977229404847186194 1.80667822153302569472 3.14159265358979323846-2.04645495709510115864i
|
|
|
|
LIMITS
|
|
0 < eps < 1
|
|
|
|
LINK LIBRARY
|
|
NUMBER *qacrd(NUMBER *x, NUMBER *eps)
|
|
COMPLEX *c_acrd(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
|
|
crd
|
|
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/
|