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diff --git a/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-trigo.tex b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-trigo.tex new file mode 100644 index 00000000000..c27a135bf0a --- /dev/null +++ b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-trigo.tex @@ -0,0 +1,760 @@ +% 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
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