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+% proflycee-tools-trigo.tex
+% Copyright 2023 Cédric Pierquet
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+
+%%------CercleTrigo
+\defKV[cercletrigo]{%
+ Rayon=\def\PLcerclerayon{#1},%
+ Epaisseur=\def\PLcerclethick{#1},%
+ EpaisseurSol=\def\PLcerclesolthick{#1},%
+ Marge=\def\PLcerclemarge{#1},%
+ TailleValeurs=\def\PLcerclevaleurs{#1},%
+ TailleAngles=\def\PLcercleangles{#1},%
+ CouleurFond=\def\PLcerclefond{#1},%
+ Decal=\def\PLcercledecal{#1},%
+ cos=\def\PLcerclevalcos{#1},%
+ sin=\def\PLcerclevalsin{#1},%
+ CouleurSol=\def\PLcerclecoleq{#1}
+}
+
+\setKVdefault[cercletrigo]{
+ Rayon=3,%
+ Marge=0.25,%
+ Decal=10pt,%
+ Epaisseur=thick,%
+ EpaisseurSol=very thick,%
+ AffAngles=true,%
+ AffTraits=true,%
+ AffValeurs=true,%
+ MoinsPi=true,%
+ TailleValeurs=\scriptsize,%
+ TailleAngles=\footnotesize,%
+ CouleurFond=white,%
+ Equationcos=false,%
+ Equationsin=false,%
+ cos=45,%
+ sin=30,%
+ CouleurSol=blue
+}
+
+\newcommand\CercleTrigo[1][]{%
+ \useKVdefault[cercletrigo]
+ \setKV[cercletrigo]{#1}
+ \tikzset{PLval/.style={inner sep=1pt,font=\PLcerclevaleurs,fill=\PLcerclefond}}
+ \tikzset{PLagl/.style={inner sep=1pt,font=\PLcercleangles,fill=\PLcerclefond}}
+ %valeurs remarquables
+ \ifboolKV[cercletrigo]{AffAngles}
+ {%valeursdudessus
+ \draw ({\PLcerclerayon},0) node[above right=2pt,font=\PLcercleangles] {0} ;
+ \draw ($(30:{\PLcerclerayon})+(30:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{6}$} ;
+ \draw ($(45:{\PLcerclerayon})+(45:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{4}$} ;
+ \draw ($(60:{\PLcerclerayon})+(60:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{3}$} ;
+ \draw (0,{\PLcerclerayon}) node[above right=2pt,PLagl] {$\tfrac{\pi}{2}$} ;
+ \draw ({-\PLcerclerayon},0) node[above left=2pt,PLagl] {$\pi$} ;
+ \draw ($(150:{\PLcerclerayon})+(150:\PLcercledecal)$) node[PLagl] {$\tfrac{5\pi}{6}$} ;
+ \draw ($(135:{\PLcerclerayon})+(135:\PLcercledecal)$) node[PLagl] {$\tfrac{3\pi}{4}$} ;
+ \draw ($(120:{\PLcerclerayon})+(120:\PLcercledecal)$) node[PLagl] {$\tfrac{2\pi}{3}$} ;
+ \draw ($(30:{\PLcerclerayon})+(30:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{6}$} ;
+ %valeursdudessous
+ \draw ($(-30:{\PLcerclerayon})+(-30:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{11}\pi}{6}$} ;
+ \draw ($(-45:{\PLcerclerayon})+(-45:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{7}\pi}{4}$} ;
+ \draw ($(-60:{\PLcerclerayon})+(-60:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{5}\pi}{3}$} ;
+ \draw (0,{-\PLcerclerayon}) node[below right=2pt,PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{3}\pi}{2}$} ;
+ \draw ($(-120:{\PLcerclerayon})+(-120:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-2}{4}\pi}{3}$} ;
+ \draw ($(-135:{\PLcerclerayon})+(-135:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-3}{5}\pi}{4}$} ;
+ \draw ($(-150:{\PLcerclerayon})+(-150:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-5}{7}\pi}{6}$} ;
+ \ifboolKV[cercletrigo]{MoinsPi}
+ {\draw ({-\PLcerclerayon},0) node[below left=2pt,PLagl] {$-\pi$} ;}
+ {\draw ({\PLcerclerayon},0) node[below right=2pt,PLagl] {$2\pi$} ;}
+ }%
+ {}
+ %tracés
+ \draw[\PLcerclethick,->,>=latex] ({-\PLcerclerayon-\PLcerclemarge},0)--({\PLcerclerayon+\PLcerclemarge},0) ;
+ \draw[\PLcerclethick,->,>=latex] (0,{-\PLcerclerayon-\PLcerclemarge})--(0,{\PLcerclerayon+\PLcerclemarge}) ;
+ \draw[\PLcerclethick] (0,0) circle[radius=\PLcerclerayon] ;
+ \draw (0,0) node[below left=2pt,PLval] {0} ;
+ %equations
+ \ifboolKV[cercletrigo]{Equationcos}
+ {%traitsdeconstructioncos
+ \draw[\PLcerclethick,dotted,gray] (-45:\PLcerclerayon) -- (135:\PLcerclerayon)
+ (-135:\PLcerclerayon) -- (45:\PLcerclerayon)
+ (30:\PLcerclerayon) -- (150:\PLcerclerayon)
+ (-30:\PLcerclerayon) -- (-150:\PLcerclerayon)
+ (-60:\PLcerclerayon)--(60:\PLcerclerayon)
+ (-120:\PLcerclerayon)--(120:\PLcerclerayon) ;
+ \draw[\PLcerclesolthick,\PLcerclecoleq] ({\PLcerclevalcos}:\PLcerclerayon)--({-\PLcerclevalcos}:\PLcerclerayon) ;
+ \filldraw[\PLcerclecoleq] ({\PLcerclevalcos}:\PLcerclerayon) circle[radius=2pt] ({-\PLcerclevalcos}:\PLcerclerayon) circle[radius=2pt] ;%
+ }
+ {}
+ \ifboolKV[cercletrigo]{Equationsin}
+ {%traitsdeconstructioncos
+ \draw[\PLcerclethick,dotted,gray] (-45:\PLcerclerayon) -- (135:\PLcerclerayon)
+ (-135:\PLcerclerayon) -- (45:\PLcerclerayon)
+ (30:\PLcerclerayon) -- (150:\PLcerclerayon)
+ (-30:\PLcerclerayon) -- (-150:\PLcerclerayon)
+ (-60:\PLcerclerayon)--(60:\PLcerclerayon)
+ (-120:\PLcerclerayon)--(120:\PLcerclerayon) ;
+ \draw[\PLcerclesolthick,\PLcerclecoleq] ({\PLcerclevalsin}:\PLcerclerayon)--({180-\PLcerclevalsin}:\PLcerclerayon) ;
+ \filldraw[\PLcerclecoleq] ({\PLcerclevalsin}:\PLcerclerayon) circle[radius=2pt] ({180-\PLcerclevalsin}:\PLcerclerayon) circle[radius=2pt] ;%
+ }
+ {}
+ %valeurs
+ \ifboolKV[cercletrigo]{AffValeurs}
+ {%
+ \draw ({0.5*\PLcerclerayon},0) node[below=2pt,PLval] {$\tfrac{1}{2}$} ;
+ \draw ({-0.5*\PLcerclerayon},0) node[below=2pt,PLval] {$-\tfrac{1}{2}$} ;
+ \draw (0,{0.5*\PLcerclerayon}) node[left=2pt,PLval] {$\tfrac{1}{2}$} ;
+ \draw (0,{-0.5*\PLcerclerayon}) node[left=2pt,PLval] {$-\tfrac{1}{2}$} ;
+ \draw ({0.866*\PLcerclerayon},0) node[below=2pt,PLval] {$\tfrac{\sqrt{3}}{2}$} ;
+ \draw ({-0.866*\PLcerclerayon},0) node[below=2pt,PLval] {$-\tfrac{\sqrt{3}}{2}$} ;
+ \draw (0,{0.866*\PLcerclerayon}) node[left=2pt,PLval] {$\tfrac{\sqrt{3}}{2}$} ;
+ \draw (0,{-0.866*\PLcerclerayon}) node[left=2pt,PLval] {$-\tfrac{\sqrt{3}}{2}$} ;
+ \draw ({0.707*\PLcerclerayon},0) node[above=2pt,PLval] {$\tfrac{\sqrt{2}}{2}$} ;
+ \draw ({-0.707*\PLcerclerayon},0) node[above=2pt,PLval] {$-\tfrac{\sqrt{2}}{2}$} ;
+ \draw (0,{0.707*\PLcerclerayon}) node[right=2pt,PLval] {$\tfrac{\sqrt{2}}{2}$} ;
+ \draw (0,{-0.707*\PLcerclerayon}) node[right=2pt,PLval] {$-\tfrac{\sqrt{2}}{2}$} ;
+ %\draw[\PLcerclethick] (0,0) circle[radius=\PLcerclerayon] ; %on retrace par dessus ?
+ }%
+ {}
+ %valeurs remarquables en dernier
+ \ifboolKV[cercletrigo]{AffTraits}
+ {%
+ \draw[\PLcerclethick,dotted,gray] (-120:\PLcerclerayon) rectangle (60:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (-150:\PLcerclerayon) rectangle (30:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (-135:\PLcerclerayon) rectangle (45:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (-120:\PLcerclerayon)--(60:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (-150:\PLcerclerayon)--(30:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (-135:\PLcerclerayon)--(45:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (120:\PLcerclerayon)--(-60:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (150:\PLcerclerayon)--(-30:\PLcerclerayon) ;
+ \draw[\PLcerclethick,dotted,gray] (135:\PLcerclerayon)--(-45:\PLcerclerayon) ;
+ }%
+ {}
+}
+
+%%------MESUREPPALE
+\setKVdefault[MesurePpale]{%
+ Crochets=false,%
+ d=false,%
+ Brut=false
+}
+
+\newcommand{\MesurePrincipale}[2][]{%fraction sous la forme a*pi/b ou entier :-)
+ \useKVdefault[MesurePpale]%
+ \setKV[MesurePpale]{#1}%
+ \StrDel{#2}{pi}[\MPargument]%
+ \IfBeginWith{#2}{pi}%
+ {\StrSubstitute{#2}{pi}{1}[\MPargument]}%
+ {}%
+ \IfBeginWith{#2}{-pi}%
+ {\StrSubstitute{#2}{pi}{1}[\MPargument]}%
+ {}%
+ %on conserve les données initiales
+ \IfSubStr{\MPargument}{/}%on coupe numérateur/dénominateur
+ { \StrCut{\MPargument}{/}\MPnumerateurinit\MPdenominateurinit }%
+ { \xdef\MPnumerateurinit{\MPargument}\xdef\MPdenominateurinit{1} }%
+ %on affiche le début, avant simplification
+ \ifboolKV[MesurePpale]{d}%
+ {\displaystyle}%
+ {}%
+ \xintifboolexpr{\MPdenominateurinit == 1}%
+ {\ifboolKV[MesurePpale]{Brut}{}{\num{\MPnumerateurinit}\pi=}}%
+ {\ifboolKV[MesurePpale]{Brut}{}{\frac{\num{\MPnumerateurinit}\pi}{\num{\MPdenominateurinit}}=}}%
+ %on simplifie puis on réduit
+ \xdef\MPsimpl{\xintPRaw{\xintIrr{\MPargument}}}%
+ %test si l'argument est une fraction ou un entier
+ \IfSubStr{\MPsimpl}{/}%
+ {\StrCut{\MPsimpl}{/}\MPnumerateur\MPdenominateur}%
+ {\xdef\MPnumerateur{\MPsimpl}\xdef\MPdenominateur{1}}%
+ %calculs
+ \xdef\MPtour{\inteval{2*\MPdenominateur}}%
+ \xdef\MPreste{\xintiiRem{\MPnumerateur}{\MPtour}}%reste
+ \xintifboolexpr{\MPreste>\MPdenominateur}%
+ {\xdef\MPreste{\inteval{\MPreste-\MPtour}}}{}%
+ \xintifboolexpr{\MPreste<-\MPdenominateur}%
+ {\xdef\MPreste{\inteval{\MPreste+\MPtour}}}{}%
+ %sortie suivant fraction ou non...
+ \xintifboolexpr{\MPdenominateur == 1}%
+ {%entier
+ \xintifboolexpr{\MPreste == 1}{\pi \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}} }{}%
+ \xintifboolexpr{\MPreste == 0}{0 \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}} }{}%
+ \xintifboolexpr{\MPreste != 0 && \MPreste != 1}{\MPreste\pi \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}} }{}%
+ }%
+ {%fraction
+ \frac{%
+ \xintifboolexpr{\xinteval{\MPreste == 1}}{}{}%
+ \xintifboolexpr{\xinteval{\MPreste == -1}}{-}{}%
+ \xintifboolexpr{\xinteval{abs(\MPreste) != 1}}{\num{\MPreste}}{}%
+ \pi}{\num{\MPdenominateur}} \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}}%
+ }%
+}
+
+%%------LIGNES TRIGOS
+\setKVdefault[Lgntrig]{%
+ d=false,%
+ Etapes=false
+}
+
+\newcommand\AffAngle[2][]{%semble OK
+ %1 = options
+ %2 = angle sous la forme a*pi/b
+ \useKVdefault[Lgntrig]%
+ \setKV[Lgntrig]{#1}%
+ \StrDel{#2}{pi}[\MPargument]%
+ \IfBeginWith{#2}{pi}%
+ {\StrSubstitute{#2}{pi}{1}[\MPargument]}%
+ {}%
+ \IfBeginWith{#2}{-pi}%
+ {\StrSubstitute{#2}{pi}{1}[\MPargument]}%
+ {}%
+ %on conserve les données initiales
+ \IfSubStr{\MPargument}{/}%on coupe numérateur/dénominateur
+ {\StrCut{\MPargument}{/}\MPnumerateurinit\MPdenominateurinit}%
+ {\xdef\MPnumerateurinit{\MPargument}\xdef\MPdenominateurinit{1}}%
+ %on affiche le début, avant simplification
+ \ifboolKV[Lgntrig]{d}{\displaystyle}{}%
+ \xintifboolexpr{\MPdenominateurinit == 1}%
+ {%
+ \xintifboolexpr{\MPnumerateurinit == 1}{\pi}{}%
+ \xintifboolexpr{\MPnumerateurinit == -1}{-\pi}{}%
+ \xintifboolexpr{\xinteval{abs(\MPnumerateurinit) != 1}}{\num{\MPnumerateurinit}\pi}{}%
+ }%
+ {%
+ \frac{%
+ \xintifboolexpr{\MPnumerateurinit == 1}{\pi}{}%
+ \xintifboolexpr{\MPnumerateurinit == -1}{-\pi}{}
+ \xintifboolexpr{\xinteval{abs(\MPnumerateurinit) != 1}}{\num{\MPnumerateurinit}\pi}{}%
+ }%
+ {%
+ \num{\MPdenominateurinit}%
+ }%
+ }%
+}
+
+\newcommand\IntSimplifMesPpale[1]{%commande interne
+ \IfSubStr{#1}{pi}%
+ {%
+ \StrDel{#1}{pi}[\tmpargument]
+ \IfBeginWith{#1}{pi}%
+ {\StrSubstitute{#1}{pi}{1}[\tmpargument]}%
+ {}%
+ \IfBeginWith{#1}{-pi}%
+ {\StrSubstitute{#1}{pi}{1}[\tmpargument]}%
+ {}%
+ }%
+ {\def\tmpargument{#1}}%
+ \IfSubStr{\tmpargument}{/}%on coupe numérateur/dénominateur
+ {\StrCut{\tmpargument}{/}\MPnumerateurinit\MPdenominateurinit}%
+ {\xdef\MPnumerateurinit{\tmpargument}\xdef\MPdenominateurinit{1}}%
+ \xdef\MPsimpl{\xintPRaw{\xintIrr{\tmpargument}}}%
+ \IfSubStr{\MPsimpl}{/}%
+ {\StrCut{\MPsimpl}{/}\MPnumerateur\MPdenominateur}%
+ {\xdef\MPnumerateur{\MPsimpl}\xdef\MPdenominateur{1}}%
+ %calculs
+ \xdef\MPtour{\inteval{2*\MPdenominateur}}%
+ \xdef\MPreste{\xintiiRem{\MPnumerateur}{\MPtour}}%reste
+ \xintifboolexpr{\MPreste>\MPdenominateur}%
+ {\xdef\MPreste{\inteval{\MPreste-\MPtour}}}{}%
+ \xintifboolexpr{\MPreste<-\MPdenominateur}%
+ {\xdef\MPreste{\inteval{\MPreste+\MPtour}}}{}%
+ \xdef\MPfrac{\MPreste/\MPdenominateur}%
+}
+
+\NewDocumentCommand\LigneTrigo{ s O{} m d() }{%
+ %* = sans l'énoncé
+ %2 = options
+ %3 = ligne
+ %4 = angle
+ \useKVdefault[Lgntrig]%
+ \setKV[Lgntrig]{#2}
+ \ifboolKV[Lgntrig]{d}{\displaystyle}{}%
+ \IntSimplifMesPpale{#4} %simplification du quotient et stockage dans \MPfrac
+ %les cas de figure [0;pi]
+ \xintifboolexpr{\MPfrac == 0}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left(\MesurePrincipale[Brut]{#4}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2-\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1/6}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1/4}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1/3}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 5/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2+\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1/2}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 7/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2-\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 2/3}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 3/4}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 5/6}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 11/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2+\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 1/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1+\sqrt{2} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 3/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1+\sqrt{2} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 5/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1-\sqrt{2} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 7/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1-\sqrt{2} }{}%
+ }%
+ {}%
+ %cas ]-pi,0[
+ \xintifboolexpr{\MPfrac == -1/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2+\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/6}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/4}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/3}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -5/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2-\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/2}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -7/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2+\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -2/3}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -3/4}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -5/6}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -11/12}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2-\sqrt{3} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1-\sqrt{2} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -3/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1-\sqrt{2} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -5/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1+\sqrt{2} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -7/8}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1+\sqrt{2} }{}%
+ }%
+ {}%
+ %les pi/5
+ \xintifboolexpr{\MPfrac == 1/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5-2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 2/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5+2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 3/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5+2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 4/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1-\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5-2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -4/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1-\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5-2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -3/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5+2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -2/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5+2\sqrt{5}} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/5}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5-2\sqrt{5}} }{}%
+ }%
+ {}%
+ %les pi/10
+ \xintifboolexpr{\MPfrac == 1/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 3/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 7/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == 9/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -1/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -3/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -7/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1+\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+ \xintifboolexpr{\MPfrac == -9/10}
+ {%
+ \ifstrequal{#3}{cos}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
+ \ifstrequal{#3}{sin}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
+ \ifstrequal{#3}{tan}%
+ {\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
+ }%
+ {}%
+}
+
+\endinput \ No newline at end of file