% proflycee-tools-trigo.tex % Copyright 2023-2024 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) ; }% {} } %%------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