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fix and improve trigonometric help files

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The trigonometric file files have had several bug fixed.

The EXAMPLE sections of trigonometric file have
been made consistent.

Added these new help files in anticipation of
the code for these new (i.e., to be written) builtin functions:

    hacovercos hacoversin havercos haversin
    ahacovercos ahacoversin ahavercos ahaversin
This commit is contained in:
Landon Curt Noll
2023-09-24 12:52:14 -07:00
parent db80afb843
commit ab95e47c0a
30 changed files with 928 additions and 176 deletions
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37
help/asec
View File

@@ -11,26 +11,33 @@ TYPES
return real
DESCRIPTION
Returns the inverse secant of x to a multiple of eps with error less in
Returns the inverse trigonometric secant of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called arcsec, is such that:
sec(asec(x)) = x
and such that:
asec(x) = acos(1/x)
This function is sometimes called arcsec.
EXAMPLE
; print asec(2, 1e-5), asec(2, 1e-10), asec(2, 1e-15), asec(2, 1e-20)
1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
; print asec(0), asec(0.5), asec(1)
Error 10453 1.31695789692481670863i 0
; print asec(-0.5), asec(-1)
3.14159265358979323846-1.31695789692481670863i 3.14159265358979323846
; print asec(.5, 1e-5), asec(.5, 1e-10), asec(.5, 1e-15), asec(.5, 1e-20)
1.31695i 1.316957897i 1.316957896924816i 1.31695789692481670863i
; print asec(5), asec(5i)
1.36943840600456582778 1.57079632679489661923+0.19869011034924140647i
; print acos(5+5i)
0.79039774680951249644-2.64919617780647114961i
; print asec(5+5i)
1.4711326239351014592+0.10033029811220500594i
; pi = pi(1e-20)
; print asec(pi/6), asec(pi/3)
1.26327680856656556836i 0.30137360974529145454
; print asec(4*pi/3)
1.32973601406082299099
LIMITS
0 < eps < 1
@@ -42,8 +49,10 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, acsc
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
versin, coversin, vercos, covercos
aversin, acoversin, avercos, acovercos
haversin, hacoversin, havercos, hacovercos
ahaversin, hacoversin, havercos, ahacovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll