% proflycee-tools-trigo.tex
% Copyright 2023-2025 Cédric Pierquet
% Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txt

%%------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,%
  AffTraitsEq=true,%
  AffValeurs=true,%
  MoinsPi=true,%
  TailleValeurs=\scriptsize,%
  TailleAngles=\footnotesize,%
  CouleurFond=white,%
  Equationcos=false,%
  Equationsin=false,%
  cos=45,%
  sin=30,%
  CouleurSol=blue,%
  ValeursTan=false
}

\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}}
  %tangente ?
  \ifboolKV[cercletrigo]{ValeursTan}%
    {%
      \draw[\PLcerclethick,dotted,gray] (30:\PLcerclerayon)--({\PLcerclerayon},{sqrt(3)/3*\PLcerclerayon}) ;
      \draw[\PLcerclethick,dotted,gray] (45:\PLcerclerayon)--({\PLcerclerayon},{\PLcerclerayon}) ;
      \draw[\PLcerclethick,dotted,gray] (60:\PLcerclerayon)--({\PLcerclerayon},{sqrt(3)*\PLcerclerayon}) ;
      \draw[\PLcerclethick,dotted,gray] (-30:\PLcerclerayon)--({\PLcerclerayon},{-sqrt(3)/3*\PLcerclerayon}) ;
      \draw[\PLcerclethick,dotted,gray] (-45:\PLcerclerayon)--({\PLcerclerayon},{-\PLcerclerayon}) ;
      \draw[\PLcerclethick,dotted,gray] (-60:\PLcerclerayon)--({\PLcerclerayon},{-sqrt(3)*\PLcerclerayon}) ;
      \draw[\PLcerclethick] ({\PLcerclerayon},{-1.8*\PLcerclerayon}) -- ({\PLcerclerayon},{1.8*\PLcerclerayon}) ;
      \ifboolKV[cercletrigo]{AffValeurs}
        {%
          \draw[] ([xshift=-2pt]{\PLcerclerayon},{\PLcerclerayon})--++(4pt,0) node[right=2pt,PLval] {$1$} ;
          \draw[] ([xshift=-2pt]{\PLcerclerayon},{-\PLcerclerayon})--++(4pt,0) node[right=2pt,PLval] {$-1$} ;
          \draw[] ([xshift=-2pt]{\PLcerclerayon},{sqrt(3)*\PLcerclerayon})--++(4pt,0) node[right=2pt,PLval] {$\sqrt{3}$} ;
          \draw[] ([xshift=-2pt]{\PLcerclerayon},{-sqrt(3)*\PLcerclerayon})--++(4pt,0) node[right=2pt,PLval] {$-\sqrt{3}$} ;
          \draw[] ([xshift=-2pt]{\PLcerclerayon},{sqrt(3)/3*\PLcerclerayon})--++(4pt,0) node[right=2pt,PLval] {$\tfrac{\sqrt{3}}{3}$} ;
          \draw[] ([xshift=-2pt]{\PLcerclerayon},{-sqrt(3)/3*\PLcerclerayon})--++(4pt,0) node[right=2pt,PLval] {$-\tfrac{\sqrt{3}}{3}$} ;
        }%
        {}%
    }%
    {}%
  %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
    \ifboolKV[cercletrigo]{AffTraitsEq}
      {%
        \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
    \ifboolKV[cercletrigo]{AffTraitsEq}
      {%
        \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) ;
  }%
  {}
}
\NewCommandCopy\pflcercletrigo\CercleTrigo

%%------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)}}%
  }%
}
\NewCommandCopy\pflmesppale\MesurePrincipale

%%------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} }{}%
    }%
    {}%
}
\NewCommandCopy\pfllignetrig\LigneTrigo

\endinput