1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
|
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
cas, cis
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/
|
