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fix and improve trigonometric help files
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
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help/vercos
16
help/vercos
@@ -14,13 +14,13 @@ DESCRIPTION
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Calculate the versed trigonometric cosine 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 verc, is equivalent to:
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This function is sometimes called verc, or vercosin, is equivalent to:
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vercos(x) = 1 + cos(x)
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EXAMPLE
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; print vercos(0.2), vercos(3/7), vercos(-31)
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1.98006657784124163112 1.90956035167416667403 1.91474235780453127896
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; print vercos(1/2), vercos(5/7), vercos(42/7)
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1.87758256189037271612 1.75556134670069659847 1.96017028665036602055
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; print vercos(1, 1e-5), vercos(1, 1e-10), vercos(1, 1e-15), vercos(1, 1e-20)
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1.5403 1.5403023059 1.54030230586814 1.5403023058681397174
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@@ -29,8 +29,8 @@ EXAMPLE
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-3.18963-9.10923i -3.189625691-9.1092278938i
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; pi = pi(1e-20)
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; print vercos(pi/3, 1e-10), vercos(pi/2, 1e-10), vercos(pi, 1e-10), vercos(3*pi/2, 1e-10)
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1.5 1 0 1
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; print vercos(pi/6), vercos(pi/2), vercos(pi)
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1.86602540378443864676 1 0
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LIMITS
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0 < eps < 1
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@@ -42,8 +42,10 @@ LINK LIBRARY
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SEE ALSO
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sin, cos, tan, cot, sec, csc
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asin, acos, atan, acot, asec, acsc
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versin, coversin, vercos, avercos
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aversin, acoversin, covercos, acovercos
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versin, coversin, 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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epsilon
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## Copyright (C) 2023 Landon Curt Noll
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