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+%D In order to support rotation over arbitrary angles, we need a sine
+%D and cosine calculator. For this purpose we borrow a few macros by
+%D David Carlisle (his trig package). Because local variables are
+%D used, I patched the macros a bit. Also, I used a few different names
+%D for variabels and macros and use existing auxiliary macros.
+
+\unprotect
+
+\chardef \@iv = 4
+\chardef \@xc = 90 % was \nin@ty
+\chardef \@clxx = 180
+\chardef \@lxxi = 71
+\mathchardef \@mmmmlxviii = 4068
+\mathchardef \@xvi@k = 16384
+
+\chardef \tr@coeffz = 72
+\chardef \tr@coefb = 42
+\mathchardef \tr@coefc = 840
+\mathchardef \tr@coefd = 5040
+
+\def\tg@series
+ {\!!dimena\@lxxi\!!dimena
+ \divide\!!dimena\@mmmmlxviii
+ \edef\!!stringa{\withoutpt\the\!!dimena}%
+ \!!dimena\!!stringa\!!dimena
+ \edef\!!stringb{\withoutpt\the\!!dimena}%
+ \divide\!!dimena\tr@coeffz
+ \advance\!!dimena\minusone\onepoint
+ \!!dimena\!!stringb\!!dimena
+ \advance\!!dimena \tr@coefb\onepoint
+ \!!dimena\!!stringb\!!dimena
+ \advance\!!dimena -\tr@coefc\onepoint
+ \!!dimena\!!stringb\!!dimena
+ \advance\!!dimena \tr@coefd\onepoint
+ \!!dimena\!!stringa\!!dimena
+ \divide\!!dimena \tr@coefd}
+
+\def\tg@reduce#1#2%
+ {\!!dimena#1#2\@xc\onepoint
+ \advance\!!dimena#2-\@clxx\onepoint
+ \!!dimena-\!!dimena
+ \tg@@sin}
+
+\def\tg@@sin
+ {\ifdim\tg@reduce>+\else\ifdim\tg@reduce<-\else
+ \tg@series
+ \fi\fi}
+
+%D Calculating a sine is a two step process: first a value is
+%D calculated, and afterwards it can be used. This saves redundant
+%D calculations.
+
+\def\calculatesin#1%
+ {{\expandafter\ifx\csname sin \number#1\endcsname\relax
+ \!!dimena#1\onepoint
+ \tg@@sin
+ \expandafter\xdef\csname sin \number#1\endcsname{\withoutpt\the\!!dimena}%
+ \fi}}
+
+\def\calculatecos#1%
+ {{\expandafter\ifx\csname cos \number#1\endcsname\relax
+ \!!dimena\@xc\onepoint
+ \advance\!!dimena-#1\onepoint
+ \tg@@sin
+ \expandafter\xdef\csname cos \number#1\endcsname{\withoutpt\the\!!dimena}%
+ \fi}}
+
+\def\calculatetan#1%
+ {{\expandafter\ifx\csname tan \number#1\endcsname\relax
+ \calculatesin{#1}%
+ \calculatecos{#1}%
+ \!!dimena\calculatedcos{#1}\onepoint
+ \divide\!!dimena\@iv
+ \!!dimenb\calculatedsin{#1}\onepoint
+ \!!dimenb\@xvi@k\!!dimenb
+ \divide\!!dimenb\!!dimena
+ \expandafter\xdef\csname tan \number#1\endcsname{\withoutpt\the\!!dimenb}%
+ \fi}}
+
+%D The results are accessed with:
+
+\def\calculatedsin#1{\csname sin \number#1\endcsname}
+\def\calculatedcos#1{\csname cos \number#1\endcsname}
+\def\calculatedtan#1{\csname tan \number#1\endcsname}
+
+%D A more save implementation would be:
+
+\def\calculatedsin#1{\executeifdefined{sin \number#1}\!!zerocount}
+\def\calculatedcos#1{\executeifdefined{cos \number#1}\!!plusone}
+\def\calculatedtan#1{\executeifdefined{tan \number#1}\!!zerocount}
+
+%D A few values are predefined, although, on todays systems there
+%D is no real reason for that. I've added the 270 ones and changed
+%D the -90 tan. Also, I prefer text (\type {\!!..} instead of
+%D counters \type {\..}.
+
+\expandafter\let\csname sin 0\endcsname\!!zerocount
+\expandafter\let\csname cos 0\endcsname\!!plusone
+\expandafter\let\csname sin 90\endcsname\!!plusone
+\expandafter\let\csname cos 90\endcsname\!!zerocount
+\expandafter\let\csname sin 180\endcsname\!!zerocount
+\expandafter\let\csname cos 180\endcsname\!!minusone
+\expandafter\let\csname sin 270\endcsname\!!minusone
+\expandafter\let\csname cos 270\endcsname\!!zerocount
+
+\expandafter\let\csname sin -90\endcsname\!!minusone
+\expandafter\let\csname cos -90\endcsname\!!zerocount
+
+\expandafter\def\csname tan 90\endcsname{\writestatus\m!systems{infinite tan +90}}
+\expandafter\def\csname tan -90\endcsname{\writestatus\m!systems{infinite tan -90}}
+
+%D Usage: \type {\calculatesin{10}} and \type {\calculatedsin{10}}
+
+\protect \endinput