% Copyright 2007 by Mark Wibrow
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Public License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.

% This file defines the trigonometric functions/functions.
%
% Much of this file is based on ideas and code (particularly 
% the old \pgfcoremath.code.tex) due to Till Tantau.
%
% Version 1.414213 29/9/2007

% \pgfmathpi
%
\pgfmathdeclarefunction{pi}{0}{\def\pgfmathresult{3.141592654}}

% \pgfmathradians 
% (for comptability with 1.18 beta, will be deprecated)
% 
% Convert #1 from radians to degrees (accurate to 1 deg).
%
\pgfmathdeclarefunction{radians}{1}{%
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}%

% \pgfmathdeg
% 
% Convert #1 from radians to degrees.
%
\pgfmathdeclarefunction{deg}{1}{%	
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}%

% \pgfmathrad
% 
% Convert #1 from degrees to radians.
%
\pgfmathdeclarefunction{rad}{1}{%	
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\pgfmath@x3.14159\pgfmath@x% 
		\divide\pgfmath@x180\relax%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}%

% \pgfmathsin
% 
% Calculate the sine of #1 (in degrees).
%
\pgfmathdeclarefunction{sin}{1}{%
	% Let #1 = a.b
	% Then sin(#1) \approx (1-b)*sin(a) + b*sin(a+1)
	%
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\advance\pgfmath@x-90pt\relax%
		\afterassignment\pgfmath@gobbletilpgfmath@
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@
		\divide\c@pgfmath@counta360\relax%
		\multiply\c@pgfmath@counta-360\relax%
		\advance\pgfmath@x\c@pgfmath@counta pt\relax%
		\ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
		\ifdim\pgfmath@x<180pt\relax%
		\else
			\pgfmath@x-\pgfmath@x%
			\advance\pgfmath@x360pt\relax%
		\fi%
		% Now 0 <= x < 179. So split x into integer and decimal...
		%
		\afterassignment\pgfmath@xa%
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
		%
		% ...if #1 is an integer, don't do anything fancy.
		\ifdim\pgfmath@xa=0pt%
			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt\relax%
		\else%
			\pgfmath@x-\pgfmath@xa%
			\advance\pgfmath@x1pt\relax%
			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
			\advance\c@pgfmath@counta1\relax%
			\expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
		\fi%
		\pgfmath@returnone\pgfmath@x%
	\endgroup
}

% \pgfmathcos
% 
% Calculate the cosine of #1 (in degrees).
%
\pgfmathdeclarefunction{cos}{1}{%
	% Let x = a.b
	% Then cos(x) \approx (1-b)*cos(a) + b*cos(a+1)
	%
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\afterassignment\pgfmath@gobbletilpgfmath@%
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% 
		\divide\c@pgfmath@counta360\relax%
		\multiply\c@pgfmath@counta-360\relax%
		\advance\pgfmath@x\c@pgfmath@counta pt\relax%
		\ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi%
		\ifdim\pgfmath@x<180pt\relax%
		\else%
			\pgfmath@x-\pgfmath@x%
			\advance\pgfmath@x360pt\relax%
		\fi%
		% Now 0 <= x < 179. So split x into integer and decimal...
		%
		\afterassignment\pgfmath@xa%
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
		%
		% ...if #1 is an integer, don't do anything fancy.
		\ifdim\pgfmath@xa=0pt%
			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt%
		\else%
			\pgfmath@x-\pgfmath@xa%
			\advance\pgfmath@x1pt\relax%
			\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
			\advance\c@pgfmath@counta1\relax%
			\ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
			\expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
		\fi%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}

% \pgfmathsincos
% 
% Calculate the sin and cosine of #1 (in degrees).
%
\def\pgfmathsincos#1{%
	\pgfmathparse{#1}%
	\expandafter\pgfmathsincos@\expandafter{\pgfmathresult}}
\def\pgfmathsincos@#1{%
	\edef\pgfmath@temparg{#1}%
	\pgfmathsin@{\pgfmath@temparg}\edef\pgfmathresulty{\pgfmathresult}%
	\pgfmathcos@{\pgfmath@temparg}\edef\pgfmathresultx{\pgfmathresult}%
}

% \pgfmathtan
% 
% Calculate the tangent of #1 (in degrees).
%
\pgfmathdeclarefunction{tan}{1}{%
	\begingroup%
		\edef\pgfmath@temparg{#1}%
		\pgfmathcos@{\pgfmath@temparg}%
		\expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
		\edef\pgfmath@tantemp{\pgfmathresult}%
		\pgfmathsin@{\pgfmath@temparg}%
		\pgfmath@x\pgfmathresult pt\relax%
		\pgfmath@x\pgfmath@tantemp\pgfmath@x%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}

% \pgfmathcosec
% 
% Calculate the cosec of #1 (in degrees).
%
\pgfmathdeclarefunction{cosec}{1}{%	
	\expandafter\pgfmathsin@\expandafter{#1}%
	\pgfmathreciprocal@{\pgfmathresult}%
}

% \pgfmathsec
% 
% Calculate the sec of #1 (in degrees).
%
\pgfmathdeclarefunction{sec}{1}{%
	\expandafter\pgfmathcos@\expandafter{#1}%
	\pgfmathreciprocal@{\pgfmathresult}%
}

% \pgfmathcot
% 
% Calculate the cotangent of #1 (in degrees).
%
\pgfmathdeclarefunction{cot}{1}{%	
	\begingroup%
		\edef\pgfmath@temparg{#1}%
		\pgfmathsin@{\pgfmath@temparg}%
		\expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
		\edef\pgfmath@tantemp{\pgfmathresult}%
		\pgfmathcos@{\pgfmath@temparg}%
		\pgfmath@x\pgfmathresult pt\relax%
		\pgfmath@x\pgfmath@tantemp\pgfmath@x%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}

% \pgfmathasin
%
% The asin of #1
%
\pgfmathdeclarefunction{asin}{1}{%
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\pgfmath@xa\pgfmath@x%
		\ifdim\pgfmath@x<0pt\relax%
			\pgfmath@x-\pgfmath@x%
		\fi%
		\pgfmath@x1000\pgfmath@x%
		\afterassignment\pgfmath@gobbletilpgfmath@%
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
		\pgfmath@x-\csname pgfmath@acos@\the\c@pgfmath@counta\endcsname pt\relax%
		\advance\pgfmath@x90pt\relax%
		\ifdim\pgfmath@xa<0pt\relax%
			\pgfmath@x-\pgfmath@x%
		\fi%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}

% \pgfmathacos
%
% The acos of #1
%	
\pgfmathdeclarefunction{acos}{1}{%
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\pgfmath@xa\pgfmath@x%
		\ifdim\pgfmath@x<0pt\relax%
			\pgfmath@x-\pgfmath@x%
		\fi%
		\pgfmath@x1000\pgfmath@x%
		\afterassignment\pgfmath@gobbletilpgfmath@%
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
		\expandafter\pgfmath@x\csname pgfmath@acos@\the\c@pgfmath@counta\endcsname pt\relax%
		\ifdim\pgfmath@xa<0pt\relax%
			\pgfmath@x-\pgfmath@x%
			\advance\pgfmath@x by180pt\relax%
		\fi%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}

\pgfmathdeclarefunction{atan}{1}{%
	\begingroup%
		\expandafter\pgfmath@x#1pt\relax%
		\pgfmath@xa\pgfmath@x%
		\ifdim\pgfmath@x<0pt\relax%
			\pgfmath@x-\pgfmath@x%
		\fi%
		\pgfmath@xb\pgfmath@x%
		\ifdim\pgfmath@x>1pt\relax%
			\edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
			\pgfmathreciprocal@{\pgfmath@temp}%
			\pgfmath@x\pgfmathresult pt\relax%
		\fi%
		\pgfmath@x1000\pgfmath@x%
		\afterassignment\pgfmath@gobbletilpgfmath@%
		\expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@%
		\ifdim\pgfmath@xb>1pt\relax%
			\expandafter\pgfmath@x\expandafter-\csname pgfmath@atan@\the\c@pgfmath@counta\endcsname pt\relax%
			\advance\pgfmath@x90pt%
		\else%
			\expandafter\pgfmath@x\csname pgfmath@atan@\the\c@pgfmath@counta\endcsname pt\relax%
		\fi%
		\ifdim\pgfmath@xa<0pt\relax%
			\pgfmath@x-\pgfmath@x%
		\fi%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%
}

\pgfmathdeclarefunction{atan2}{2}{%
	\begingroup%
		\pgfmath@x=#1pt\relax%
		\ifdim\pgfmath@x<0pt\relax%
			\pgfmath@x=-\pgfmath@x%
		\fi%
		\ifdim\pgfmath@x<0.001pt\relax%
			\ifdim#2pt<0pt\relax%
				\pgfmath@x=-90pt\relax%
			\else%
				\ifdim#2pt>0pt\relax%
					\pgfmath@x=90pt\relax%
				\else%
					\pgfmath@x=0pt\relax%
				\fi%
			\fi%
		\else%
			\pgfmathdivide@{#2}{#1}%
			\expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
			\pgfmath@x=\pgfmathresult pt\relax%
			\ifdim#2pt<0pt\relax%
				\ifdim#1pt<0pt\relax%
					\advance\pgfmath@x by-180pt\relax%
				\fi%
			\else%
				\ifdim#1pt<0pt\relax%
					\advance\pgfmath@x by180pt\relax%
				\fi%
			\fi%
		\fi%
		\pgfmath@returnone\pgfmath@x%
	\endgroup%		
}

\def\pgfmath@def#1#2#3{\expandafter\def\csname pgfmath@#1@#2\endcsname{#3}}
\pgfmath@def{cos}{0}{1.00000}		\pgfmath@def{cos}{1}{0.99985}
\pgfmath@def{cos}{2}{0.99939}		\pgfmath@def{cos}{3}{0.99863}
\pgfmath@def{cos}{4}{0.99756}		\pgfmath@def{cos}{5}{0.99619}
\pgfmath@def{cos}{6}{0.99452}		\pgfmath@def{cos}{7}{0.99255}
\pgfmath@def{cos}{8}{0.99027}		\pgfmath@def{cos}{9}{0.98769}
\pgfmath@def{cos}{10}{0.98481}		\pgfmath@def{cos}{11}{0.98163}
\pgfmath@def{cos}{12}{0.97815}		\pgfmath@def{cos}{13}{0.97437}
\pgfmath@def{cos}{14}{0.97030}		\pgfmath@def{cos}{15}{0.96593}
\pgfmath@def{cos}{16}{0.96126}		\pgfmath@def{cos}{17}{0.95630}
\pgfmath@def{cos}{18}{0.95106}		\pgfmath@def{cos}{19}{0.94552}
\pgfmath@def{cos}{20}{0.93969}		\pgfmath@def{cos}{21}{0.93358}
\pgfmath@def{cos}{22}{0.92718}		\pgfmath@def{cos}{23}{0.92050}
\pgfmath@def{cos}{24}{0.91355}		\pgfmath@def{cos}{25}{0.90631}
\pgfmath@def{cos}{26}{0.89879}		\pgfmath@def{cos}{27}{0.89101}
\pgfmath@def{cos}{28}{0.88295}		\pgfmath@def{cos}{29}{0.87462}
\pgfmath@def{cos}{30}{0.86603}		\pgfmath@def{cos}{31}{0.85717}
\pgfmath@def{cos}{32}{0.84805}		\pgfmath@def{cos}{33}{0.83867}
\pgfmath@def{cos}{34}{0.82904}		\pgfmath@def{cos}{35}{0.81915}
\pgfmath@def{cos}{36}{0.80902}		\pgfmath@def{cos}{37}{0.79864}
\pgfmath@def{cos}{38}{0.78801}		\pgfmath@def{cos}{39}{0.77715}
\pgfmath@def{cos}{40}{0.76604}		\pgfmath@def{cos}{41}{0.75471}
\pgfmath@def{cos}{42}{0.74314}		\pgfmath@def{cos}{43}{0.73135}
\pgfmath@def{cos}{44}{0.71934}		\pgfmath@def{cos}{45}{0.70711}
\pgfmath@def{cos}{46}{0.69466}		\pgfmath@def{cos}{47}{0.68200}
\pgfmath@def{cos}{48}{0.66913}		\pgfmath@def{cos}{49}{0.65606}
\pgfmath@def{cos}{50}{0.64279}		\pgfmath@def{cos}{51}{0.62932}
\pgfmath@def{cos}{52}{0.61566}		\pgfmath@def{cos}{53}{0.60182}
\pgfmath@def{cos}{54}{0.58779}		\pgfmath@def{cos}{55}{0.57358}
\pgfmath@def{cos}{56}{0.55919}		\pgfmath@def{cos}{57}{0.54464}
\pgfmath@def{cos}{58}{0.52992}		\pgfmath@def{cos}{59}{0.51504}
\pgfmath@def{cos}{60}{0.50000}		\pgfmath@def{cos}{61}{0.48481}
\pgfmath@def{cos}{62}{0.46947}		\pgfmath@def{cos}{63}{0.45399}
\pgfmath@def{cos}{64}{0.43837}		\pgfmath@def{cos}{65}{0.42262}
\pgfmath@def{cos}{66}{0.40674}		\pgfmath@def{cos}{67}{0.39073}
\pgfmath@def{cos}{68}{0.37461}		\pgfmath@def{cos}{69}{0.35837}
\pgfmath@def{cos}{70}{0.34202}		\pgfmath@def{cos}{71}{0.32557}
\pgfmath@def{cos}{72}{0.30902}		\pgfmath@def{cos}{73}{0.29237}
\pgfmath@def{cos}{74}{0.27564}		\pgfmath@def{cos}{75}{0.25882}
\pgfmath@def{cos}{76}{0.24192}		\pgfmath@def{cos}{77}{0.22495}
\pgfmath@def{cos}{78}{0.20791}		\pgfmath@def{cos}{79}{0.19081}
\pgfmath@def{cos}{80}{0.17365}		\pgfmath@def{cos}{81}{0.15643}
\pgfmath@def{cos}{82}{0.13917}		\pgfmath@def{cos}{83}{0.12187}
\pgfmath@def{cos}{84}{0.10453}		\pgfmath@def{cos}{85}{0.08716}
\pgfmath@def{cos}{86}{0.06976}		\pgfmath@def{cos}{87}{0.05234}
\pgfmath@def{cos}{88}{0.03490}		\pgfmath@def{cos}{89}{0.01745}
\pgfmath@def{cos}{90}{0.00000}		\pgfmath@def{cos}{91}{-0.01745}
\pgfmath@def{cos}{92}{-0.03490}		\pgfmath@def{cos}{93}{-0.05234}
\pgfmath@def{cos}{94}{-0.06976}		\pgfmath@def{cos}{95}{-0.08716}
\pgfmath@def{cos}{96}{-0.10453}		\pgfmath@def{cos}{97}{-0.12187}
\pgfmath@def{cos}{98}{-0.13917}		\pgfmath@def{cos}{99}{-0.15643}
\pgfmath@def{cos}{100}{-0.17365}		\pgfmath@def{cos}{101}{-0.19081}
\pgfmath@def{cos}{102}{-0.20791}		\pgfmath@def{cos}{103}{-0.22495}
\pgfmath@def{cos}{104}{-0.24192}		\pgfmath@def{cos}{105}{-0.25882}
\pgfmath@def{cos}{106}{-0.27564}		\pgfmath@def{cos}{107}{-0.29237}
\pgfmath@def{cos}{108}{-0.30902}		\pgfmath@def{cos}{109}{-0.32557}
\pgfmath@def{cos}{110}{-0.34202}		\pgfmath@def{cos}{111}{-0.35837}
\pgfmath@def{cos}{112}{-0.37461}		\pgfmath@def{cos}{113}{-0.39073}
\pgfmath@def{cos}{114}{-0.40674}		\pgfmath@def{cos}{115}{-0.42262}
\pgfmath@def{cos}{116}{-0.43837}		\pgfmath@def{cos}{117}{-0.45399}
\pgfmath@def{cos}{118}{-0.46947}		\pgfmath@def{cos}{119}{-0.48481}
\pgfmath@def{cos}{120}{-0.50000}		\pgfmath@def{cos}{121}{-0.51504}
\pgfmath@def{cos}{122}{-0.52992}		\pgfmath@def{cos}{123}{-0.54464}
\pgfmath@def{cos}{124}{-0.55919}		\pgfmath@def{cos}{125}{-0.57358}
\pgfmath@def{cos}{126}{-0.58779}		\pgfmath@def{cos}{127}{-0.60182}
\pgfmath@def{cos}{128}{-0.61566}		\pgfmath@def{cos}{129}{-0.62932}
\pgfmath@def{cos}{130}{-0.64279}		\pgfmath@def{cos}{131}{-0.65606}
\pgfmath@def{cos}{132}{-0.66913}		\pgfmath@def{cos}{133}{-0.68200}
\pgfmath@def{cos}{134}{-0.69466}		\pgfmath@def{cos}{135}{-0.70711}
\pgfmath@def{cos}{136}{-0.71934}		\pgfmath@def{cos}{137}{-0.73135}
\pgfmath@def{cos}{138}{-0.74314}		\pgfmath@def{cos}{139}{-0.75471}
\pgfmath@def{cos}{140}{-0.76604}		\pgfmath@def{cos}{141}{-0.77715}
\pgfmath@def{cos}{142}{-0.78801}		\pgfmath@def{cos}{143}{-0.79864}
\pgfmath@def{cos}{144}{-0.80902}		\pgfmath@def{cos}{145}{-0.81915}
\pgfmath@def{cos}{146}{-0.82904}		\pgfmath@def{cos}{147}{-0.83867}
\pgfmath@def{cos}{148}{-0.84805}		\pgfmath@def{cos}{149}{-0.85717}
\pgfmath@def{cos}{150}{-0.86603}		\pgfmath@def{cos}{151}{-0.87462}
\pgfmath@def{cos}{152}{-0.88295}		\pgfmath@def{cos}{153}{-0.89101}
\pgfmath@def{cos}{154}{-0.89879}		\pgfmath@def{cos}{155}{-0.90631}
\pgfmath@def{cos}{156}{-0.91355}		\pgfmath@def{cos}{157}{-0.92050}
\pgfmath@def{cos}{158}{-0.92718}		\pgfmath@def{cos}{159}{-0.93358}
\pgfmath@def{cos}{160}{-0.93969}		\pgfmath@def{cos}{161}{-0.94552}
\pgfmath@def{cos}{162}{-0.95106}		\pgfmath@def{cos}{163}{-0.95630}
\pgfmath@def{cos}{164}{-0.96126}		\pgfmath@def{cos}{165}{-0.96593}
\pgfmath@def{cos}{166}{-0.97030}		\pgfmath@def{cos}{167}{-0.97437}
\pgfmath@def{cos}{168}{-0.97815}		\pgfmath@def{cos}{169}{-0.98163}
\pgfmath@def{cos}{170}{-0.98481}		\pgfmath@def{cos}{171}{-0.98769}
\pgfmath@def{cos}{172}{-0.99027}		\pgfmath@def{cos}{173}{-0.99255}
\pgfmath@def{cos}{174}{-0.99452}		\pgfmath@def{cos}{175}{-0.99619}
\pgfmath@def{cos}{176}{-0.99756}		\pgfmath@def{cos}{177}{-0.99863}
\pgfmath@def{cos}{178}{-0.99939}		\pgfmath@def{cos}{179}{-0.99985}
\pgfmath@def{cos}{180}{-1.00000}	   \pgfmath@def{cos}{181}{-0.99985}

\pgfmath@def{cosfrac}{0}{1.00000}		\pgfmath@def{cosfrac}{1}{0.99995}
\pgfmath@def{cosfrac}{2}{0.99980}		\pgfmath@def{cosfrac}{3}{0.99955}
\pgfmath@def{cosfrac}{4}{0.99920}		\pgfmath@def{cosfrac}{5}{0.99875}
\pgfmath@def{cosfrac}{6}{0.99820}		\pgfmath@def{cosfrac}{7}{0.99755}
\pgfmath@def{cosfrac}{8}{0.99681}		\pgfmath@def{cosfrac}{9}{0.99597}
\pgfmath@def{cosfrac}{10}{0.99503}		\pgfmath@def{cosfrac}{11}{0.99400}
\pgfmath@def{cosfrac}{12}{0.99287}		\pgfmath@def{cosfrac}{13}{0.99165}
\pgfmath@def{cosfrac}{14}{0.99034}		\pgfmath@def{cosfrac}{15}{0.98893}
\pgfmath@def{cosfrac}{16}{0.98744}		\pgfmath@def{cosfrac}{17}{0.98585}
\pgfmath@def{cosfrac}{18}{0.98418}		\pgfmath@def{cosfrac}{19}{0.98242}
\pgfmath@def{cosfrac}{20}{0.98058}		\pgfmath@def{cosfrac}{21}{0.97865}
\pgfmath@def{cosfrac}{22}{0.97664}		\pgfmath@def{cosfrac}{23}{0.97455}
\pgfmath@def{cosfrac}{24}{0.97238}		\pgfmath@def{cosfrac}{25}{0.97014}
\pgfmath@def{cosfrac}{26}{0.96782}		\pgfmath@def{cosfrac}{27}{0.96542}
\pgfmath@def{cosfrac}{28}{0.96296}		\pgfmath@def{cosfrac}{29}{0.96042}
\pgfmath@def{cosfrac}{30}{0.95782}		\pgfmath@def{cosfrac}{31}{0.95515}
\pgfmath@def{cosfrac}{32}{0.95242}		\pgfmath@def{cosfrac}{33}{0.94962}
\pgfmath@def{cosfrac}{34}{0.94677}		\pgfmath@def{cosfrac}{35}{0.94385}
\pgfmath@def{cosfrac}{36}{0.94088}		\pgfmath@def{cosfrac}{37}{0.93786}
\pgfmath@def{cosfrac}{38}{0.93478}		\pgfmath@def{cosfrac}{39}{0.93165}
\pgfmath@def{cosfrac}{40}{0.92847}		\pgfmath@def{cosfrac}{41}{0.92525}
\pgfmath@def{cosfrac}{42}{0.92198}		\pgfmath@def{cosfrac}{43}{0.91866}
\pgfmath@def{cosfrac}{44}{0.91531}		\pgfmath@def{cosfrac}{45}{0.91192}
\pgfmath@def{cosfrac}{46}{0.90849}		\pgfmath@def{cosfrac}{47}{0.90502}
\pgfmath@def{cosfrac}{48}{0.90152}		\pgfmath@def{cosfrac}{49}{0.89799}
\pgfmath@def{cosfrac}{50}{0.89442}		\pgfmath@def{cosfrac}{51}{0.89083}
\pgfmath@def{cosfrac}{52}{0.88721}		\pgfmath@def{cosfrac}{53}{0.88357}
\pgfmath@def{cosfrac}{54}{0.87990}		\pgfmath@def{cosfrac}{55}{0.87621}
\pgfmath@def{cosfrac}{56}{0.87250}		\pgfmath@def{cosfrac}{57}{0.86877}
\pgfmath@def{cosfrac}{58}{0.86503}		\pgfmath@def{cosfrac}{59}{0.86126}
\pgfmath@def{cosfrac}{60}{0.85749}		\pgfmath@def{cosfrac}{61}{0.85370}
\pgfmath@def{cosfrac}{62}{0.84990}		\pgfmath@def{cosfrac}{63}{0.84609}
\pgfmath@def{cosfrac}{64}{0.84227}		\pgfmath@def{cosfrac}{65}{0.83844}
\pgfmath@def{cosfrac}{66}{0.83460}		\pgfmath@def{cosfrac}{67}{0.83077}
\pgfmath@def{cosfrac}{68}{0.82692}		\pgfmath@def{cosfrac}{69}{0.82308}
\pgfmath@def{cosfrac}{70}{0.81923}		\pgfmath@def{cosfrac}{71}{0.81538}
\pgfmath@def{cosfrac}{72}{0.81153}		\pgfmath@def{cosfrac}{73}{0.80768}
\pgfmath@def{cosfrac}{74}{0.80384}		\pgfmath@def{cosfrac}{75}{0.80000}
\pgfmath@def{cosfrac}{76}{0.79616}		\pgfmath@def{cosfrac}{77}{0.79232}
\pgfmath@def{cosfrac}{78}{0.78850}		\pgfmath@def{cosfrac}{79}{0.78468}
\pgfmath@def{cosfrac}{80}{0.78086}		\pgfmath@def{cosfrac}{81}{0.77706}
\pgfmath@def{cosfrac}{82}{0.77326}		\pgfmath@def{cosfrac}{83}{0.76948}
\pgfmath@def{cosfrac}{84}{0.76570}		\pgfmath@def{cosfrac}{85}{0.76193}
\pgfmath@def{cosfrac}{86}{0.75818}		\pgfmath@def{cosfrac}{87}{0.75444}
\pgfmath@def{cosfrac}{88}{0.75071}		\pgfmath@def{cosfrac}{89}{0.74699}
\pgfmath@def{cosfrac}{90}{0.74329}		\pgfmath@def{cosfrac}{91}{0.73960}
\pgfmath@def{cosfrac}{92}{0.73593}		\pgfmath@def{cosfrac}{93}{0.73227}
\pgfmath@def{cosfrac}{94}{0.72862}		\pgfmath@def{cosfrac}{95}{0.72499}
\pgfmath@def{cosfrac}{96}{0.72138}		\pgfmath@def{cosfrac}{97}{0.71779}
\pgfmath@def{cosfrac}{98}{0.71421}		\pgfmath@def{cosfrac}{99}{0.71065}
\pgfmath@def{cosfrac}{100}{0.70710}	

% Oh No! Some really loooooong tables.
\pgfmath@def{atan}{0}{0.00000}		\pgfmath@def{atan}{1}{0.05729}
\pgfmath@def{atan}{2}{0.11459}		\pgfmath@def{atan}{3}{0.17188}
\pgfmath@def{atan}{4}{0.22918}		\pgfmath@def{atan}{5}{0.28647}
\pgfmath@def{atan}{6}{0.34377}		\pgfmath@def{atan}{7}{0.40106}
\pgfmath@def{atan}{8}{0.45835}		\pgfmath@def{atan}{9}{0.51564}
\pgfmath@def{atan}{10}{0.57293}		\pgfmath@def{atan}{11}{0.63022}
\pgfmath@def{atan}{12}{0.68751}		\pgfmath@def{atan}{13}{0.74480}
\pgfmath@def{atan}{14}{0.80208}		\pgfmath@def{atan}{15}{0.85937}
\pgfmath@def{atan}{16}{0.91665}		\pgfmath@def{atan}{17}{0.97393}
\pgfmath@def{atan}{18}{1.03121}		\pgfmath@def{atan}{19}{1.08848}
\pgfmath@def{atan}{20}{1.14576}		\pgfmath@def{atan}{21}{1.20303}
\pgfmath@def{atan}{22}{1.26030}		\pgfmath@def{atan}{23}{1.31757}
\pgfmath@def{atan}{24}{1.37483}		\pgfmath@def{atan}{25}{1.43209}
\pgfmath@def{atan}{26}{1.48935}		\pgfmath@def{atan}{27}{1.54661}
\pgfmath@def{atan}{28}{1.60386}		\pgfmath@def{atan}{29}{1.66111}
\pgfmath@def{atan}{30}{1.71835}		\pgfmath@def{atan}{31}{1.77560}
\pgfmath@def{atan}{32}{1.83284}		\pgfmath@def{atan}{33}{1.89007}
\pgfmath@def{atan}{34}{1.94730}		\pgfmath@def{atan}{35}{2.00453}
\pgfmath@def{atan}{36}{2.06175}		\pgfmath@def{atan}{37}{2.11897}
\pgfmath@def{atan}{38}{2.17619}		\pgfmath@def{atan}{39}{2.23340}
\pgfmath@def{atan}{40}{2.29061}		\pgfmath@def{atan}{41}{2.34781}
\pgfmath@def{atan}{42}{2.40500}		\pgfmath@def{atan}{43}{2.46220}
\pgfmath@def{atan}{44}{2.51938}		\pgfmath@def{atan}{45}{2.57657}
\pgfmath@def{atan}{46}{2.63374}		\pgfmath@def{atan}{47}{2.69092}
\pgfmath@def{atan}{48}{2.74808}		\pgfmath@def{atan}{49}{2.80524}
\pgfmath@def{atan}{50}{2.86240}		\pgfmath@def{atan}{51}{2.91955}
\pgfmath@def{atan}{52}{2.97669}		\pgfmath@def{atan}{53}{3.03383}
\pgfmath@def{atan}{54}{3.09097}		\pgfmath@def{atan}{55}{3.14809}
\pgfmath@def{atan}{56}{3.20521}		\pgfmath@def{atan}{57}{3.26232}
\pgfmath@def{atan}{58}{3.31943}		\pgfmath@def{atan}{59}{3.37653}
\pgfmath@def{atan}{60}{3.43363}		\pgfmath@def{atan}{61}{3.49071}
\pgfmath@def{atan}{62}{3.54779}		\pgfmath@def{atan}{63}{3.60487}
\pgfmath@def{atan}{64}{3.66193}		\pgfmath@def{atan}{65}{3.71899}
\pgfmath@def{atan}{66}{3.77604}		\pgfmath@def{atan}{67}{3.83308}
\pgfmath@def{atan}{68}{3.89012}		\pgfmath@def{atan}{69}{3.94715}
\pgfmath@def{atan}{70}{4.00417}		\pgfmath@def{atan}{71}{4.06118}
\pgfmath@def{atan}{72}{4.11819}		\pgfmath@def{atan}{73}{4.17518}
\pgfmath@def{atan}{74}{4.23217}		\pgfmath@def{atan}{75}{4.28915}
\pgfmath@def{atan}{76}{4.34612}		\pgfmath@def{atan}{77}{4.40308}
\pgfmath@def{atan}{78}{4.46004}		\pgfmath@def{atan}{79}{4.51698}
\pgfmath@def{atan}{80}{4.57392}		\pgfmath@def{atan}{81}{4.63084}
\pgfmath@def{atan}{82}{4.68776}		\pgfmath@def{atan}{83}{4.74467}
\pgfmath@def{atan}{84}{4.80157}		\pgfmath@def{atan}{85}{4.85846}
\pgfmath@def{atan}{86}{4.91534}		\pgfmath@def{atan}{87}{4.97221}
\pgfmath@def{atan}{88}{5.02907}		\pgfmath@def{atan}{89}{5.08592}
\pgfmath@def{atan}{90}{5.14276}		\pgfmath@def{atan}{91}{5.19959}
\pgfmath@def{atan}{92}{5.25641}		\pgfmath@def{atan}{93}{5.31322}
\pgfmath@def{atan}{94}{5.37002}		\pgfmath@def{atan}{95}{5.42681}
\pgfmath@def{atan}{96}{5.48359}		\pgfmath@def{atan}{97}{5.54035}
\pgfmath@def{atan}{98}{5.59711}		\pgfmath@def{atan}{99}{5.65385}
\pgfmath@def{atan}{100}{5.71059}		\pgfmath@def{atan}{101}{5.76731}
\pgfmath@def{atan}{102}{5.82402}		\pgfmath@def{atan}{103}{5.88072}
\pgfmath@def{atan}{104}{5.93741}		\pgfmath@def{atan}{105}{5.99409}
\pgfmath@def{atan}{106}{6.05075}		\pgfmath@def{atan}{107}{6.10741}
\pgfmath@def{atan}{108}{6.16405}		\pgfmath@def{atan}{109}{6.22068}
\pgfmath@def{atan}{110}{6.27729}		\pgfmath@def{atan}{111}{6.33390}
\pgfmath@def{atan}{112}{6.39049}		\pgfmath@def{atan}{113}{6.44707}
\pgfmath@def{atan}{114}{6.50364}		\pgfmath@def{atan}{115}{6.56019}
\pgfmath@def{atan}{116}{6.61673}		\pgfmath@def{atan}{117}{6.67326}
\pgfmath@def{atan}{118}{6.72978}		\pgfmath@def{atan}{119}{6.78628}
\pgfmath@def{atan}{120}{6.84277}		\pgfmath@def{atan}{121}{6.89924}
\pgfmath@def{atan}{122}{6.95571}		\pgfmath@def{atan}{123}{7.01216}
\pgfmath@def{atan}{124}{7.06859}		\pgfmath@def{atan}{125}{7.12501}
\pgfmath@def{atan}{126}{7.18142}		\pgfmath@def{atan}{127}{7.23781}
\pgfmath@def{atan}{128}{7.29419}		\pgfmath@def{atan}{129}{7.35056}
\pgfmath@def{atan}{130}{7.40691}		\pgfmath@def{atan}{131}{7.46324}
\pgfmath@def{atan}{132}{7.51957}		\pgfmath@def{atan}{133}{7.57587}
\pgfmath@def{atan}{134}{7.63217}		\pgfmath@def{atan}{135}{7.68844}
\pgfmath@def{atan}{136}{7.74471}		\pgfmath@def{atan}{137}{7.80095}
\pgfmath@def{atan}{138}{7.85719}		\pgfmath@def{atan}{139}{7.91340}
\pgfmath@def{atan}{140}{7.96961}		\pgfmath@def{atan}{141}{8.02579}
\pgfmath@def{atan}{142}{8.08196}		\pgfmath@def{atan}{143}{8.13812}
\pgfmath@def{atan}{144}{8.19426}		\pgfmath@def{atan}{145}{8.25038}
\pgfmath@def{atan}{146}{8.30649}		\pgfmath@def{atan}{147}{8.36258}
\pgfmath@def{atan}{148}{8.41866}		\pgfmath@def{atan}{149}{8.47472}
\pgfmath@def{atan}{150}{8.53076}		\pgfmath@def{atan}{151}{8.58679}
\pgfmath@def{atan}{152}{8.64280}		\pgfmath@def{atan}{153}{8.69879}
\pgfmath@def{atan}{154}{8.75477}		\pgfmath@def{atan}{155}{8.81073}
\pgfmath@def{atan}{156}{8.86667}		\pgfmath@def{atan}{157}{8.92260}
\pgfmath@def{atan}{158}{8.97851}		\pgfmath@def{atan}{159}{9.03440}
\pgfmath@def{atan}{160}{9.09027}		\pgfmath@def{atan}{161}{9.14613}
\pgfmath@def{atan}{162}{9.20197}		\pgfmath@def{atan}{163}{9.25779}
\pgfmath@def{atan}{164}{9.31359}		\pgfmath@def{atan}{165}{9.36938}
\pgfmath@def{atan}{166}{9.42515}		\pgfmath@def{atan}{167}{9.48090}
\pgfmath@def{atan}{168}{9.53663}		\pgfmath@def{atan}{169}{9.59235}
\pgfmath@def{atan}{170}{9.64804}		\pgfmath@def{atan}{171}{9.70372}
\pgfmath@def{atan}{172}{9.75938}		\pgfmath@def{atan}{173}{9.81502}
\pgfmath@def{atan}{174}{9.87064}		\pgfmath@def{atan}{175}{9.92624}
\pgfmath@def{atan}{176}{9.98182}		\pgfmath@def{atan}{177}{10.03739}
\pgfmath@def{atan}{178}{10.09294}		\pgfmath@def{atan}{179}{10.14846}
\pgfmath@def{atan}{180}{10.20397}		\pgfmath@def{atan}{181}{10.25946}
\pgfmath@def{atan}{182}{10.31493}		\pgfmath@def{atan}{183}{10.37037}
\pgfmath@def{atan}{184}{10.42580}		\pgfmath@def{atan}{185}{10.48121}
\pgfmath@def{atan}{186}{10.53660}		\pgfmath@def{atan}{187}{10.59197}
\pgfmath@def{atan}{188}{10.64732}		\pgfmath@def{atan}{189}{10.70265}
\pgfmath@def{atan}{190}{10.75796}		\pgfmath@def{atan}{191}{10.81325}
\pgfmath@def{atan}{192}{10.86852}		\pgfmath@def{atan}{193}{10.92377}
\pgfmath@def{atan}{194}{10.97900}		\pgfmath@def{atan}{195}{11.03420}
\pgfmath@def{atan}{196}{11.08939}		\pgfmath@def{atan}{197}{11.14456}
\pgfmath@def{atan}{198}{11.19970}		\pgfmath@def{atan}{199}{11.25483}
\pgfmath@def{atan}{200}{11.30993}		\pgfmath@def{atan}{201}{11.36501}
\pgfmath@def{atan}{202}{11.42007}		\pgfmath@def{atan}{203}{11.47511}
\pgfmath@def{atan}{204}{11.53013}		\pgfmath@def{atan}{205}{11.58512}
\pgfmath@def{atan}{206}{11.64010}		\pgfmath@def{atan}{207}{11.69505}
\pgfmath@def{atan}{208}{11.74998}		\pgfmath@def{atan}{209}{11.80489}
\pgfmath@def{atan}{210}{11.85977}		\pgfmath@def{atan}{211}{11.91464}
\pgfmath@def{atan}{212}{11.96948}		\pgfmath@def{atan}{213}{12.02430}
\pgfmath@def{atan}{214}{12.07910}		\pgfmath@def{atan}{215}{12.13388}
\pgfmath@def{atan}{216}{12.18863}		\pgfmath@def{atan}{217}{12.24336}
\pgfmath@def{atan}{218}{12.29807}		\pgfmath@def{atan}{219}{12.35275}
\pgfmath@def{atan}{220}{12.40741}		\pgfmath@def{atan}{221}{12.46205}
\pgfmath@def{atan}{222}{12.51667}		\pgfmath@def{atan}{223}{12.57126}
\pgfmath@def{atan}{224}{12.62583}		\pgfmath@def{atan}{225}{12.68038}
\pgfmath@def{atan}{226}{12.73490}		\pgfmath@def{atan}{227}{12.78940}
\pgfmath@def{atan}{228}{12.84388}		\pgfmath@def{atan}{229}{12.89833}
\pgfmath@def{atan}{230}{12.95276}		\pgfmath@def{atan}{231}{13.00717}
\pgfmath@def{atan}{232}{13.06155}		\pgfmath@def{atan}{233}{13.11590}
\pgfmath@def{atan}{234}{13.17024}		\pgfmath@def{atan}{235}{13.22455}
\pgfmath@def{atan}{236}{13.27883}		\pgfmath@def{atan}{237}{13.33309}
\pgfmath@def{atan}{238}{13.38733}		\pgfmath@def{atan}{239}{13.44154}
\pgfmath@def{atan}{240}{13.49573}		\pgfmath@def{atan}{241}{13.54989}
\pgfmath@def{atan}{242}{13.60403}		\pgfmath@def{atan}{243}{13.65814}
\pgfmath@def{atan}{244}{13.71223}		\pgfmath@def{atan}{245}{13.76630}
\pgfmath@def{atan}{246}{13.82034}		\pgfmath@def{atan}{247}{13.87435}
\pgfmath@def{atan}{248}{13.92834}		\pgfmath@def{atan}{249}{13.98230}
\pgfmath@def{atan}{250}{14.03624}		\pgfmath@def{atan}{251}{14.09015}
\pgfmath@def{atan}{252}{14.14404}		\pgfmath@def{atan}{253}{14.19790}
\pgfmath@def{atan}{254}{14.25174}		\pgfmath@def{atan}{255}{14.30555}
\pgfmath@def{atan}{256}{14.35933}		\pgfmath@def{atan}{257}{14.41309}
\pgfmath@def{atan}{258}{14.46682}		\pgfmath@def{atan}{259}{14.52053}
\pgfmath@def{atan}{260}{14.57421}		\pgfmath@def{atan}{261}{14.62787}
\pgfmath@def{atan}{262}{14.68149}		\pgfmath@def{atan}{263}{14.73510}
\pgfmath@def{atan}{264}{14.78867}		\pgfmath@def{atan}{265}{14.84222}
\pgfmath@def{atan}{266}{14.89575}		\pgfmath@def{atan}{267}{14.94924}
\pgfmath@def{atan}{268}{15.00271}		\pgfmath@def{atan}{269}{15.05615}
\pgfmath@def{atan}{270}{15.10957}		\pgfmath@def{atan}{271}{15.16296}
\pgfmath@def{atan}{272}{15.21632}		\pgfmath@def{atan}{273}{15.26966}
\pgfmath@def{atan}{274}{15.32297}		\pgfmath@def{atan}{275}{15.37625}
\pgfmath@def{atan}{276}{15.42950}		\pgfmath@def{atan}{277}{15.48273}
\pgfmath@def{atan}{278}{15.53593}		\pgfmath@def{atan}{279}{15.58910}
\pgfmath@def{atan}{280}{15.64224}		\pgfmath@def{atan}{281}{15.69536}
\pgfmath@def{atan}{282}{15.74845}		\pgfmath@def{atan}{283}{15.80151}
\pgfmath@def{atan}{284}{15.85454}		\pgfmath@def{atan}{285}{15.90755}
\pgfmath@def{atan}{286}{15.96052}		\pgfmath@def{atan}{287}{16.01347}
\pgfmath@def{atan}{288}{16.06640}		\pgfmath@def{atan}{289}{16.11929}
\pgfmath@def{atan}{290}{16.17215}		\pgfmath@def{atan}{291}{16.22499}
\pgfmath@def{atan}{292}{16.27780}		\pgfmath@def{atan}{293}{16.33058}
\pgfmath@def{atan}{294}{16.38333}		\pgfmath@def{atan}{295}{16.43605}
\pgfmath@def{atan}{296}{16.48875}		\pgfmath@def{atan}{297}{16.54142}
\pgfmath@def{atan}{298}{16.59405}		\pgfmath@def{atan}{299}{16.64666}
\pgfmath@def{atan}{300}{16.69924}		\pgfmath@def{atan}{301}{16.75179}
\pgfmath@def{atan}{302}{16.80431}		\pgfmath@def{atan}{303}{16.85680}
\pgfmath@def{atan}{304}{16.90927}		\pgfmath@def{atan}{305}{16.96170}
\pgfmath@def{atan}{306}{17.01411}		\pgfmath@def{atan}{307}{17.06648}
\pgfmath@def{atan}{308}{17.11883}		\pgfmath@def{atan}{309}{17.17114}
\pgfmath@def{atan}{310}{17.22343}		\pgfmath@def{atan}{311}{17.27569}
\pgfmath@def{atan}{312}{17.32792}		\pgfmath@def{atan}{313}{17.38012}
\pgfmath@def{atan}{314}{17.43228}		\pgfmath@def{atan}{315}{17.48442}
\pgfmath@def{atan}{316}{17.53653}		\pgfmath@def{atan}{317}{17.58861}
\pgfmath@def{atan}{318}{17.64066}		\pgfmath@def{atan}{319}{17.69268}
\pgfmath@def{atan}{320}{17.74467}		\pgfmath@def{atan}{321}{17.79663}
\pgfmath@def{atan}{322}{17.84855}		\pgfmath@def{atan}{323}{17.90045}
\pgfmath@def{atan}{324}{17.95232}		\pgfmath@def{atan}{325}{18.00416}
\pgfmath@def{atan}{326}{18.05596}		\pgfmath@def{atan}{327}{18.10774}
\pgfmath@def{atan}{328}{18.15949}		\pgfmath@def{atan}{329}{18.21120}
\pgfmath@def{atan}{330}{18.26289}		\pgfmath@def{atan}{331}{18.31454}
\pgfmath@def{atan}{332}{18.36616}		\pgfmath@def{atan}{333}{18.41775}
\pgfmath@def{atan}{334}{18.46931}		\pgfmath@def{atan}{335}{18.52084}
\pgfmath@def{atan}{336}{18.57234}		\pgfmath@def{atan}{337}{18.62381}
\pgfmath@def{atan}{338}{18.67525}		\pgfmath@def{atan}{339}{18.72665}
\pgfmath@def{atan}{340}{18.77803}		\pgfmath@def{atan}{341}{18.82937}
\pgfmath@def{atan}{342}{18.88068}		\pgfmath@def{atan}{343}{18.93196}
\pgfmath@def{atan}{344}{18.98321}		\pgfmath@def{atan}{345}{19.03443}
\pgfmath@def{atan}{346}{19.08562}		\pgfmath@def{atan}{347}{19.13677}
\pgfmath@def{atan}{348}{19.18789}		\pgfmath@def{atan}{349}{19.23898}
\pgfmath@def{atan}{350}{19.29004}		\pgfmath@def{atan}{351}{19.34107}
\pgfmath@def{atan}{352}{19.39206}		\pgfmath@def{atan}{353}{19.44303}
\pgfmath@def{atan}{354}{19.49396}		\pgfmath@def{atan}{355}{19.54486}
\pgfmath@def{atan}{356}{19.59572}		\pgfmath@def{atan}{357}{19.64656}
\pgfmath@def{atan}{358}{19.69736}		\pgfmath@def{atan}{359}{19.74813}
\pgfmath@def{atan}{360}{19.79887}		\pgfmath@def{atan}{361}{19.84958}
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