<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%%%
% Trigonom\'etrie
%%%
\def\filedateTrigo{2024/08/04}%
\def\fileversionTrigo{0.1}%
\message{-- \filedateTrigo\space v\fileversionTrigo}%
%
\def\MPFigTrigo#1#2#3#4#5#6#7#8{%
  \ifluatex
%  \mplibcodeinherit{enable}
  \mplibforcehmode
  \begin{mplibcode}
    defaultcolormodel := \useKV[ClesTrigo]{ModeleCouleur};
    u:=\useKV[ClesTrigo]{Echelle};
    pair A,B,C,O,I,D,E,F;%
    % On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure
    A=u*(1,1);
    B-A=u*(3,0);
    C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
    % On d\'efinit le centre du cercle circonscrit
    O - .5[A,B] = whatever * (B-A) rotated 90;
    O - .5[B,C] = whatever * (C-B) rotated 90;
    % On tourne pour \'eventuellement moins de lassitude :)
    A:=A rotatedabout(O,#8);
    B:=B rotatedabout(O,#8);
    C:=C rotatedabout(O,#8);
    % On d\'efinit le centre du cercle inscrit
    (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C];
    (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C];
    % on dessine \`a main lev\'ee :)
    path triangle;
    triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
    % on d\'efinit l'angle droit
    D-B=7*unitvector(C-B);
    F-B=7*unitvector(A-B);
    E-D=F-B;
    draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
    % L'angle :)
    path cc;
    cc=fullcircle scaled 1u;
    % on marque les angles
    picture MAngle;
    MAngle=image(
    draw (cc shifted A);
    );
    draw MAngle;
    clip currentpicture to triangle;
    draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)};
    draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)};
    draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
    % on labelise
    picture z;
    label(btex #1 etex,1.15[O,A]);
    label(btex #2 etex,1.15[O,B]);
    label(btex #3 etex,1.15[O,C]);
    label(btex \ang{#7} etex,A+0.95u*unitvector(I-A));
    decalage:=3mm;
    if #6&lt;0:
    else:
    if angle(1/2[A,C]-B)&gt;0:
      if #6=0:
        label(btex ? etex,1.1[B,1/2[A,C]]);
      else:
        label(btex \num{#6} etex,1.2[B,1/2[A,C]]);
      fi;
    else:
      if #6=0:
        label(btex ? etex,1.1[B,1/2[A,C]]);
      else:
        label(btex \num{#6} etex,1.2[B,1/2[A,C]]);
      fi;
    fi;
  fi;   
  if #4&lt;0:
  else:
    if angle(1/2[B,C]-A)&gt;0:
      if #4=0:
        label(btex ? etex,1/2[B,C]-decalage*(unitvector(A-B)));
      else:
        label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B)));
      fi;
    else:
      if #4=0:
        label(btex ? etex,1/2[B,C]-decalage*(unitvector(A-B)));
      else:
        label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B)));
      fi;
    fi;
  fi;
  if #5&lt;0:
  else:
    if angle(1/2[A,B]-C)&gt;0:
      if #5=0:
        label(btex ? etex,1/2[A,B]-decalage*(unitvector(C-B)));
      else:
        label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B)));
      fi;
    else:
      if #5=0:
        label(btex ? etex,1/2[A,B]-decalage*(unitvector(C-B)));
      else:
        label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B)));
      fi;
    fi;
    fi;
  \end{mplibcode}
%  \mplibcodeinherit{disable}
  \else
  \begin{mpost}[mpsettings={u:=\useKV[ClesTrigo]{Echelle};}]
    pair A,B,C,O,I,D,E,F;%
    % On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure
    A=u*(1,1);
    B-A=u*(3,0);
    C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
    % On d\'efinit le centre du cercle circonscrit
    O - .5[A,B] = whatever * (B-A) rotated 90;
    O - .5[B,C] = whatever * (C-B) rotated 90;
    % On tourne pour \'eventuellement moins de lassitude :)
    A:=A rotatedabout(O,#8);
    B:=B rotatedabout(O,#8);
    C:=C rotatedabout(O,#8);
    % On d\'efinit le centre du cercle inscrit
    (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C];
    (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C];
    % on dessine \`a main lev\'ee :)
    path triangle;
    triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
    % on d\'efinit l'angle droit
    D-B=7*unitvector(C-B);
    F-B=7*unitvector(A-B);
    E-D=F-B;
    draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
    % L'angle :)
    path cc;
    cc=fullcircle scaled 1u;
    % on marque les angles
    picture MAngle;
    MAngle=image(
    draw (cc shifted A);
    % draw (cc shifted B);
    % draw (cc shifted C);
    );
    draw MAngle;
    clip currentpicture to triangle;
    draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)};
    draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)};
    draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
    % on labelise
    picture z;
    label(btex #1 etex,1.15[O,A]);
    label(btex #2 etex,1.15[O,B]);
    label(btex #3 etex,1.15[O,C]);
    label(btex \ang{#7} etex,A+0.95u*unitvector(I-A));
    decalage:=3mm;
    if #6&lt;0:
    else:
    if angle(1/2[A,C]-B)&gt;0:
      if #6=0:
        label(btex ? etex rotated angle(C-A),1.1[B,1/2[A,C]]);
      else:
        label(btex \num{#6} etex rotated angle(C-A),1.2[B,1/2[A,C]]);
      fi;
    else:
      if #6=0:
        label(btex ? etex rotated angle(A-C),1.1[B,1/2[A,C]]);
      else:
        label(btex \num{#6} etex rotated angle(A-C),1.2[B,1/2[A,C]]);
      fi;
    fi;
  fi;   
  if #4&lt;0:
  else:
    if angle(1/2[B,C]-A)&gt;0:
      if #4=0:
        label(btex ? etex rotated(angle(B-C)),1/2[B,C]-decalage*(unitvector(A-B)));
      else:
        label(btex \num{#4} etex rotated(angle(B-C)),1/2[B,C]-decalage*(unitvector(A-B)));
      fi;
    else:
      if #4=0:
        label(btex ? etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B)));
      else:
        label(btex \num{#4} etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B)));
      fi;
    fi;
  fi;
  if #5&lt;0:
  else:
    if angle(1/2[A,B]-C)&gt;0:
      if #5=0:
        label(btex ? etex rotated angle(A-B),1/2[A,B]-decalage*(unitvector(C-B)));
      else:
        label(btex \num{#5} etex rotated angle(A-B),1/2[A,B]-decalage*(unitvector(C-B)));
      fi;
    else:
      if #5=0:
        label(btex ? etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B)));
      else:
        label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B)));
      fi;
    fi;
  fi;
\end{mpost}
\fi
}

\def\MPFigTrigoAngle#1#2#3#4#5#6#7{%
  % #1 A
  % #2 B
  % #3 C
  % #4 opp
  % #5 adj
  % #6 hyp
  % #7 angle de rotation
  \ifluatex
%  \mplibcodeinherit{enable}
   \mplibforcehmode
   \begin{mplibcode}
     defaultcolormodel := \useKV[ClesTrigo]{ModeleCouleur};
    u:=\useKV[ClesTrigo]{Echelle};
  pair A,B,C,O,I,D,E,F;%
  % On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure
  A=u*(1,1);
  B-A=u*(3,0);
  C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
    % On d\'efinit le centre du cercle circonscrit
  O - .5[A,B] = whatever * (B-A) rotated 90;
  O - .5[B,C] = whatever * (C-B) rotated 90;
  % On tourne pour \'eventuellement moins de lassitude :)
  A:=A rotatedabout(O,#7);
  B:=B rotatedabout(O,#7);
  C:=C rotatedabout(O,#7);
  % On d\'efinit le centre du cercle inscrit
  (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C];
  (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C];
    %on dessine \`a main lev\'ee :)
  path triangle;
  triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
  %on d\'efinit l'angle droit
  D-B=7*unitvector(C-B);
  F-B=7*unitvector(A-B);
  E-D=F-B;
  draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
  %L'angle :)
  path cc;
  cc=fullcircle scaled 1u;
  % on marque les angles
  picture MAngle;
  MAngle=image(
  draw (cc shifted A);
  );
  draw MAngle;
  clip currentpicture to triangle;
  draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)};
  draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)};
  draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
  % on labelise
  label(btex #1 etex,1.15[O,A]);
  label(btex #2 etex,1.15[O,B]);
  label(btex #3 etex,1.15[O,C]);
  label(btex ? etex,A+0.95u*unitvector(I-A));
  decalage:=3mm;
  if #6&gt;0:
  if angle(1/2[A,C]-B)&gt;0:
    label(btex \num{#6} etex,1.2[B,1/2[A,C]]);
  else:
  label(btex \num{#6} etex,1.2[B,1/2[A,C]]);
  fi;
  fi;
  if #4&gt;0:
  if angle(1/2[B,C]-A)&gt;0:
   label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B)));
  else:
    label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B)));
    fi;
    fi;
    if #5&gt;0:
  if angle(1/2[A,B]-C)&gt;0:
    label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B)));
  else:
  label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B)));
  fi;
  fi;
\end{mplibcode}
%\mplibcodeinherit{disable}
  \else
  \begin{mpost}[mpsettings={u:=\useKV[ClesTrigo]{Echelle};}]
      u:=1cm;
  pair A,B,C,O,I,D,E,F;%
    %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure
  A=u*(1,1);
  B-A=u*(3,0);
  C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
    % On d\'efinit le centre du cercle circonscrit
  O - .5[A,B] = whatever * (B-A) rotated 90;
  O - .5[B,C] = whatever * (C-B) rotated 90;
    % On tourne pour \'eventuellement moins de lassitude :)
  A:=A rotatedabout(O,#7);
  B:=B rotatedabout(O,#7);
  C:=C rotatedabout(O,#7);
    % On d\'efinit le centre du cercle inscrit
  (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C];
  (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C];
    %on dessine \`a main lev\'ee :)
  path triangle;
  triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
  %on d\'efinit l'angle droit
  D-B=7*unitvector(C-B);
  F-B=7*unitvector(A-B);
  E-D=F-B;
  draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
  %L'angle :)
  path cc;
  cc=fullcircle scaled 1u;
    % on marque les angles
  picture MAngle;
  MAngle=image(
      draw (cc shifted A);
    );
  draw MAngle;
  clip currentpicture to triangle;
  draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)};
  draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)};
  draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
    %on labelise
  label(btex #1 etex,1.15[O,A]);
  label(btex #2 etex,1.15[O,B]);
  label(btex #3 etex,1.15[O,C]);
  label(btex ? etex,A+0.95u*unitvector(I-A));
  decalage:=3mm;
  if #6&gt;0:
  if angle(1/2[A,C]-B)&gt;0:
    label(btex \num{#6} etex,1.2[B,1/2[A,C]]);
  else:
  label(btex \num{#6} etex,1.2[B,1/2[A,C]]);
  fi;
  fi;
  if #4&gt;0:
  if angle(1/2[B,C]-A)&gt;0:
   label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B)));
  else:
    label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B)));
    fi;
    fi;
    if #5&gt;0:
  if angle(1/2[A,B]-C)&gt;0:
    label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B)));
  else:
  label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B)));
  fi;
  fi;
\end{mpost}
\fi
}

\setKVdefault[ClesTrigo]{Angle=0,Propor=false,Figure=false,FigureSeule=false,ValeurExacte=false,Precision=2,Unite=cm,Sinus=false,Cosinus=false,Tangente=false,Perso=false,Echelle=1cm,ModeleCouleur=5}%

\newcommand\RedactionTrigo{}%

\newcommand\TrigoCalculs[5][]{%
  \setKV[ClesTrigo]{#1}%
  % #1 Cl\'es
  % #2 Nom du triangle ABC, rectangle en B, angle connu ou pas : BAC
  % #3 Longueur #4 Longueur #5 angle
  % On d\'efinit les points
  \DeclareSIUnit{\PfCTrigoUnit}{\useKV[ClesTrigo]{Unite}}%
  \StrMid{#2}{1}{1}[\NomA]%
  \StrMid{#2}{2}{2}[\NomB]%
  \StrMid{#2}{3}{3}[\NomC]%
  \xdef\NomTriangle{\NomA\NomB\NomC}%
  \xdef\NomAngleDroit{\NomB}%
  \xdef\NomSommetA{\NomA}%
  \xdef\NomSommetB{\NomB}%
  \xdef\NomSommetC{\NomC}%
  \ifboolKV[ClesTrigo]{Perso}{%
    \RedactionTrigo%
  }{%
    Dans le triangle $\NomA\NomB\NomC$, rectangle en $\NomB$, on a :%
  }%
  \ifboolKV[ClesTrigo]{Cosinus}{%
    \ifx\bla#3\bla%on calcule le c\^ot\'e adjacent
    \xdef\ResultatTrigo{\fpeval{round(#4*cosd(#5),\useKV[ClesTrigo]{Precision})}}%
   \ifboolKV[ClesTrigo]{Propor}{%
     \begin{align*}
       \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&amp;=\NomA\NomB\\
       \num{#4}\times\cos(\ang{#5})&amp;=\NomA\NomB%\\
       \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\
       \SI{\fpeval{round(#4*cosd(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}&amp;\IfInteger{\fpeval{round(#4*cosd(#5),9)}}{=}{\approx}\NomA\NomB}
      \end{align*}%
    }{%
      \begin{align*}
        \cos(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomA\NomB}{\NomA\NomC}\\
        \cos(\ang{#5})&amp;=\frac{\NomA\NomB}{\num{#4}}\\
        \num{#4}\times\cos(\ang{#5})&amp;=\NomA\NomB%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \SI{\fpeval{round(#4*cosd(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}&amp;\IfInteger{\fpeval{round(#4*cosd(#5),9)}}{=}{\approx}\NomA\NomB}%
      \end{align*}
    }%
    \else%
    \ifx\bla#4\bla%on calcule l'hypoth\'enuse
    \xdef\ResultatTrigo{\fpeval{round(#3/cosd(#5),\useKV[ClesTrigo]{Precision})}}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&amp;=\NomA\NomB\\
        \NomA\NomC\times\cos(\ang{#5})&amp;=\num{#3}\\
        \NomA\NomC&amp;=\frac{\num{#3}}{\cos(\ang{#5})}%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \NomA\NomC&amp;\IfInteger{\fpeval{round(#3/cosd(#5),9)}}{=}{\approx}\SI{\fpeval{round(#3/cosd(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}}%
      \end{align*}
    }{%
      \begin{align*}
        \cos(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomA\NomB}{\NomA\NomC}\\
        \cos(\ang{#5})&amp;=\frac{\num{#3}}{\NomA\NomC}\\
        \NomA\NomC&amp;=\frac{\num{#3}}{\cos(\ang{#5})}%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \NomA\NomC&amp;\IfInteger{\fpeval{round(#3/cosd(#5),9)}}{=}{\approx}\SI{\fpeval{round(#3/cosd(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}}%
      \end{align*}%
    }%
    \else%on calcule l'angle
    \xdef\ResultatTrigo{\fpeval{round(acosd(#3/#4),\useKV[ClesTrigo]{Precision})}}%
    \setKV[ClesTrigo]{Precision=0}%
    \setKV[ClesTrigo]{#1}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&amp;=\NomA\NomB\\
        \num{#4}\times\cos(\widehat{\NomB\NomA\NomC})&amp;=\num{#3}\\
        \cos(\widehat{\NomB\NomA\NomC})&amp;=\frac{\num{#3}}{\num{#4}}\\
        \widehat{\NomB\NomA\NomC}&amp;\IfInteger{\fpeval{round(acosd(#3/#4),9)}}{=}{\approx}\ang{\fpeval{round(acosd(#3/#4),\useKV[ClesTrigo]{Precision})}}%
      \end{align*}%
    }{%
      \begin{align*}
        \cos(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomA\NomB}{\NomA\NomC}\\
        \cos(\widehat{\NomB\NomA\NomC})&amp;=\frac{\num{#3}}{\num{#4}}\\
        \widehat{\NomB\NomA\NomC}&amp;\IfInteger{\fpeval{round(acosd(#3/#4),9)}}{=}{\approx}\ang{\fpeval{round(acosd(#3/#4),\useKV[ClesTrigo]{Precision})}}%
      \end{align*}%
    }%
    \fi%
    \fi%
  }{}%
  \ifboolKV[ClesTrigo]{Sinus}{%
    \ifx\bla#3\bla%on calcule le c\^ot\'e oppos\'e
    \xdef\ResultatTrigo{\fpeval{round(#4*sind(#5),\useKV[ClesTrigo]{Precision})}}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&amp;=\NomB\NomC\\
        \num{#4}\times\sin(\ang{#5})&amp;=\NomB\NomC%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \SI{\fpeval{round(#4*sind(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}&amp;\IfInteger{\fpeval{round(#4*sind(#5),9)}}{=}{\approx}\NomB\NomC}%
      \end{align*}%
    }{%
      \begin{align*}
        \sin(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomB\NomC}{\NomA\NomC}\\
        \sin(\ang{#5})&amp;=\frac{\NomB\NomC}{\num{#4}}\\
        \num{#4}\times\sin(\ang{#5})&amp;=\NomB\NomC%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \SI{\fpeval{round(#4*sind(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}&amp;\IfInteger{\fpeval{round(#4*sind(#5),9)}}{=}{\approx}\NomB\NomC}%
      \end{align*}%
    }%
    \else
    \ifx\bla#4\bla%on calcule l'hypoth\'enuse
    \xdef\ResultatTrigo{\fpeval{round(#3/sind(#5),\useKV[ClesTrigo]{Precision})}}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&amp;=\NomB\NomC\\
        \NomA\NomC\times\sin(\ang{#5})&amp;=\num{#3}\\
        \NomA\NomC&amp;=\frac{\num{#3}}{\sin(\ang{#5})}%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \NomA\NomC&amp;\IfInteger{\fpeval{round(#3/sind(#5),9)}}{=}{\approx}\SI{\fpeval{round(#3/sind(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}}%
      \end{align*}%
    }{%
      \begin{align*}
        \sin(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomB\NomC}{\NomA\NomC}\\
        \sin(\ang{#5})&amp;=\frac{\num{#3}}{\NomA\NomC}\\
        \NomA\NomC&amp;=\frac{\num{#3}}{\sin(\ang{#5})}%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \NomA\NomC&amp;\IfInteger{\fpeval{round(#3/sind(#5),9)}}{=}{\approx}\SI{\fpeval{round(#3/sind(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}}%
      \end{align*}%
    }%
    \else%on calcule l'angle
    \xdef\ResultatTrigo{\fpeval{round(asind(#3/#4),\useKV[ClesTrigo]{Precision})}}%
    \setKV[ClesTrigo]{Precision=0}%
    \setKV[ClesTrigo]{#1}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&amp;=\NomB\NomC\\
        \num{#4}\times\sin(\widehat{\NomB\NomA\NomC})&amp;=\num{#3}\\
        \sin(\widehat{\NomB\NomA\NomC})&amp;=\frac{\num{#3}}{\num{#4}}\\
        \widehat{\NomB\NomA\NomC}&amp;\IfInteger{\fpeval{round(asind(#3/#4),9)}}{=}{\approx}\ang{\fpeval{round(asind(#3/#4),\useKV[ClesTrigo]{Precision})}}%
      \end{align*}%
    }{%
      \begin{align*}
        \sin(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomB\NomC}{\NomA\NomC}\\
        \sin(\widehat{\NomB\NomA\NomC})&amp;=\frac{\num{#3}}{\num{#4}}\\
        \widehat{\NomB\NomA\NomC}&amp;\IfInteger{\fpeval{round(asind(#3/#4),9)}}{=}{\approx}\ang{\fpeval{round(asind(#3/#4),\useKV[ClesTrigo]{Precision})}}%
      \end{align*}%
    }%
    \fi%
    \fi%
  }{}%
  \ifboolKV[ClesTrigo]{Tangente}{%
    \ifx\bla#3\bla%on calcule le c\^ot\'e oppos\'e
    \xdef\ResultatTrigo{\fpeval{round(#4*tand(#5),\useKV[ClesTrigo]{Precision})}}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&amp;=\NomB\NomC\\%
        \num{#4}\times\tan(\ang{#5})&amp;=\NomB\NomC%\\%
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \SI{\fpeval{round(#4*tand(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}&amp;\IfInteger{\fpeval{round(#4*tand(#5),9)}}{=}{\approx}\NomB\NomC}%
      \end{align*}%
    }{%
      \begin{align*}
        \tan(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomB\NomC}{\NomA\NomB}\\
        \tan(\ang{#5})&amp;=\frac{\NomB\NomC}{\num{#4}}\\
        \num{#4}\times\tan(\ang{#5})&amp;=\NomB\NomC%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \SI{\fpeval{round(#4*tand(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}&amp;\IfInteger{\fpeval{round(#4*tand(#5),9)}}{=}{\approx}\NomB\NomC}%
      \end{align*}%
    }%
    \else
    \ifx\bla#4\bla%on calcule l'adjacent
    \xdef\ResultatTrigo{\fpeval{round(#3/tand(#5),\useKV[ClesTrigo]{Precision})}}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&amp;=\NomB\NomC\\
        \NomA\NomB\times\tan(\ang{#5})&amp;=\num{#3}\\
        \NomA\NomB&amp;=\frac{\num{#3}}{\tan(\ang{#5})}%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \NomA\NomB&amp;\IfInteger{\fpeval{round(#3/tand(#5),9)}}{=}{\approx}\SI{\fpeval{round(#3/tand(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}}%
      \end{align*}%
    }{%
      \begin{align*}
        \tan(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomB\NomC}{\NomA\NomB}\\
        \tan(\ang{#5})&amp;=\frac{\num{#3}}{\NomA\NomB}\\
        \NomA\NomB&amp;=\frac{\num{#3}}{\tan(\ang{#5})}%\\
        \ifboolKV[ClesTrigo]{ValeurExacte}{}{\\%
        \NomA\NomB&amp;\IfInteger{\fpeval{round(#3/tand(#5),9)}}{=}{\approx}\SI{\fpeval{round(#3/tand(#5),\useKV[ClesTrigo]{Precision})}}{\PfCTrigoUnit}}%
      \end{align*}%
    }%
    \else%on calcule l'angle
    \setKV[ClesTrigo]{Precision=0}%
    \setKV[ClesTrigo]{#1}%
    \xdef\ResultatTrigo{\fpeval{round(atand(#3/#4),\useKV[ClesTrigo]{Precision})}}%
    \ifboolKV[ClesTrigo]{Propor}{%
      \begin{align*}
        \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&amp;=\NomB\NomC\\
        \num{#4}\times\tan(\widehat{\NomB\NomA\NomC})&amp;=\num{#3}\\
        \tan(\widehat{\NomB\NomA\NomC})&amp;=\frac{\num{#3}}{\num{#4}}\\
        \widehat{\NomB\NomA\NomC}&amp;\IfInteger{\fpeval{round(atand(#3/#4),9)}}{=}{\approx}\ang{\fpeval{round(atand(#3/#4),\useKV[ClesTrigo]{Precision})}}%
      \end{align*}%
    }{%
      \begin{align*}
        \tan(\widehat{\NomB\NomA\NomC})&amp;=\frac{\NomB\NomC}{\NomA\NomB}\\
        \tan(\widehat{\NomB\NomA\NomC})&amp;=\frac{\num{#3}}{\num{#4}}\\
        \widehat{\NomB\NomA\NomC}&amp;\IfInteger{\fpeval{round(atand(#3/#4),9)}}{=}{\approx}\ang{\fpeval{round(atand(#3/#4),\useKV[ClesTrigo]{Precision})}}%
      \end{align*}%
    }%
    \fi%
    \fi%
  }{}%
}%

\newcommand\Trigo[5][]{%
  \useKVdefault[ClesTrigo]%
  \setKV[ClesTrigo]{#1}%
  % #1 Cl\'es
  % #2 Nom du triangle ABC, rectangle en B, angle connu ou pas : BAC
  % #3 Longueur #4 Longueur #5 angle
  % On d\'efinit les points
  \StrMid{#2}{1}{1}[\NomA]%
  \StrMid{#2}{2}{2}[\NomB]%
  \StrMid{#2}{3}{3}[\NomC]%
  % On r\'edige
  \ifboolKV[ClesTrigo]{FigureSeule}{%
    \ifx\bla#5\bla%
    \ifboolKV[ClesTrigo]{Cosinus}{%
      \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{-1}{#3}{#4}{\useKV[ClesTrigo]{Angle}}
    }{}%
    \ifboolKV[ClesTrigo]{Sinus}{%
      \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{-1}{#4}{\useKV[ClesTrigo]{Angle}}
    }{}%
    \ifboolKV[ClesTrigo]{Tangente}{%
      \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{-1}{\useKV[ClesTrigo]{Angle}}
    }{}%
    \else%}{%figure pour calculer une longueur
    \ifboolKV[ClesTrigo]{Cosinus}{%
      \ifx\bla#3\bla%adjacent inconnu
      \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{0}{#4}{#5}{\useKV[ClesTrigo]{Angle}}
      \else
      \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{#3}{0}{#5}{\useKV[ClesTrigo]{Angle}}
      \fi
    }{}%
    \ifboolKV[ClesTrigo]{Sinus}{%
      \ifx\bla#3\bla%adjacent inconnu
      \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{-1}{#4}{#5}{\useKV[ClesTrigo]{Angle}}
      \else
      \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{-1}{0}{#5}{\useKV[ClesTrigo]{Angle}}
      \fi
    }{}%
    \ifboolKV[ClesTrigo]{Tangente}{%
      \ifx\bla#3\bla%adjacent inconnu
      \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{#4}{-1}{#5}{\useKV[ClesTrigo]{Angle}}
      \else%
      \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{0}{-1}{#5}{\useKV[ClesTrigo]{Angle}}
      \fi%
    }{}%
    \fi%
  }{%
    \ifboolKV[ClesTrigo]{Figure}{%
      \begin{multicols}{2}%
        {\em La figure est donn\'ee \`a titre indicatif.}%
        \ifx\bla#5\bla%
        \ifboolKV[ClesTrigo]{Cosinus}{%
          \begin{center}
            \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{-1}{#3}{#4}{\useKV[ClesTrigo]{Angle}}
          \end{center}
        }{}%
        \ifboolKV[ClesTrigo]{Sinus}{%
          \begin{center}
            \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{-1}{#4}{\useKV[ClesTrigo]{Angle}}
          \end{center}
        }{}%
        \ifboolKV[ClesTrigo]{Tangente}{%
          \begin{center}
            \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{-1}{\useKV[ClesTrigo]{Angle}}
          \end{center}
        }{}%
        \else%}{%figure pour calculer une longueur
        \ifboolKV[ClesTrigo]{Cosinus}{%
          \ifx\bla#3\bla%adjacent inconnu
          \begin{center}
            \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{0}{#4}{#5}{\useKV[ClesTrigo]{Angle}}
          \end{center}
          \else
          \begin{center}
            \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{#3}{0}{#5}{\useKV[ClesTrigo]{Angle}}
          \end{center}
          \fi
        }{}%
        \ifboolKV[ClesTrigo]{Sinus}{%
          \ifx\bla#3\bla%adjacent inconnu
          \begin{center}
            \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{-1}{#4}{#5}{\useKV[ClesTrigo]{Angle}}
          \end{center}
          \else
          \begin{center}
            \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{-1}{0}{#5}{\useKV[ClesTrigo]{Angle}}
          \end{center}
          \fi
        }{}%
        \ifboolKV[ClesTrigo]{Tangente}{%
          \ifx\bla#3\bla%adjacent inconnu
          \begin{center}
            \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{#4}{-1}{#5}{\useKV[ClesTrigo]{Angle}}
          \end{center}
          \else%
          \begin{center}
            \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{0}{-1}{#5}{\useKV[ClesTrigo]{Angle}}
          \end{center}
          \fi%
        }{}%
        \fi%
        \par\columnbreak\par
        \TrigoCalculs[#1]{#2}{#3}{#4}{#5}%
      \end{multicols}
    }{%
      \TrigoCalculs[#1]{#2}{#3}{#4}{#5}%
    }%
  }%
}%</pre></body></html>