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import work from year 2016-2017

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Benjamin Bertrand
2017-06-16 09:49:23 +03:00
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3e/Geometrie/Triangle_rectange/AL7MA20TEPA0111-Sequence-07.pdf Normal file
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3e/Geometrie/Triangle_rectange/Etape 1 problème et retour sur cosinus.odt Normal file
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
% Title Page
\titre{Définition du cosinus}
\classe{Troisième}
\date{Janvier 2017}
\pagestyle{empty}
\newcommand{\lexo}{%
\setcounter{exo}{0}
\begin{Exo}[Reproduction de triangles]
\begin{enumerate}
\item Tracer les agrandissements ou les réductions des triangles suivants pour que les hypothénuses mesurent:
\begin{center}
5cm \qquad 8cm \qquad 12cm \qquad 15cm
\end{center}
\includegraphics[scale=0.7]{./fig/triangle_repro}
\item Mesurer la longueur du côté adjacents pour compléter le tableau.
\begin{tabular}{|*{6}{p{2.5cm}|}}
\hline
Hypothénuse & 5 & 8 & 10 & 12 & 15 \\
\hline
Adjacent & & & & & \\
\hline
\end{tabular}
\item Ce tableau est-il un tableau de proportionnalité?
\item Comment peut-on calculer la longueur du côté adjacent quand l'hypothénuse mesure 10cm?
\end{enumerate}
\end{Exo}
}
\begin{document}
\lexo
\vfill
\lexo
\vfill
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Notes autour du chapitre sur les triangles rectangles
#####################################################
:date: 2016-11-26
:modified: 2017-01-20
:tags: Geometrie, Trigonometrie, Pythagore
:category: 3e
:authors: Bertrand Benjamin
:summary: Notes sur le chapitre sur les outils pour calculer des éléments dans un triangle rectangle.
Étape 1: Théorème de Pythagore
------------------------------
À la fin d'un cours, pendant 10min, seul puis en groupe, on écrit tout ce que l'on se rappelle sur le théorème de Pythagore.
Cahier de bord: On rédige le théorème de Pythagore en précisant le vocabulaire.
On fait quelques exercices techniques pour apprendre à rédiger et utiliser ce théorème.
`Pythagore sur la durée <./pb_duree_triangle_rectangle.pdf>`_
Étape 2: Découverte du Cosinus
------------------------------
On trace des copies agrandies ou réduites de triangles rectangles et on complète un tableau avec les mesures de l'hypoténuse et du côté adjacents pour remarquer que c'est un tableau de proportionnalité. Le rapport ne dépend que de l'angle, on l'appellera le cosinus de l'angle.
`Reproduction de triangles pour définir le cosinus <./definition_cos.pdf>`_
Ce travail est fait en équipe et on partage la classe en 3. Chaque partie s'occupera d'un seul angle.
On laisse une trace sur le cahier de bord pour donner la définition du cosinus d'un angle.
Voici un exemple de production d'élèves: `production d'élèves <./prod_eleves_cos.pdf>`_
Étape 3: Calculer des longueurs avec le cosinus
-----------------------------------------------
On donne un exercice de calcul de longueur. Les élèves doivent exploiter la trace laissée dans le cahier de bord pour produire une réponse. Le travail se fait seul puis en groupe. Une mise en commun en plénière permet d'améliorer les rédactions et d'en produire une de référence que l'on inscrit dans le cahier de bord.
On reproduit ce genre d'exercices, sur plusieurs cours.
Étape 4: Calculer un angle avec le cosinus
------------------------------------------
De la même manière, on pose la question de retrouver la mesure de l'angle. Si la question n'est pas soulevée par les élèves, on pose la question de l'inversion du cosinus et on explique la fonction *arccos* en prenant bien soin de s'assurer que les élèves sachent l'utiliser sur leur calculatrice.
On reproduit ce genre d'exercices, sur plusieurs cours.
Étape 5 et suivantes: pour aller plus loin
------------------------------------------
`Problèmes autour des angles <./Etape 1 problème et retour sur cosinus.odt>`_
Une `activité autour de l'escargot de Pythagore <./escargot_pythagore.odt>`_ avec une ouverture sur le tableur.

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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
% Title Page
\titre{Introduction à la trigonométrie}
\classe{Troisième}
\date{Janvier 2017}
\pagestyle{empty}
\geometry{left=5mm,right=5mm, bottom= 10mm, top=10mm}
\begin{document}
Compléter le tableau suivant en fonction des triangles.
\begin{tabular}{|c|*{6}{c|}}
\hline
Triangle & Hypoténuse & coté adjacent & coté opposé & angle & $\frac{\mbox{coté adjacent}}{\mbox{Hypoténuse}}$ & $\frac{\mbox{coté opposé}}{\mbox{Hypoténuse}}$ \\
\hline
ABC & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
\hline
DEF & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
\hline
GHI & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
\hline
JKL & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
\hline
MNP & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
\hline
\end{tabular}
\begin{center}
\includegraphics[scale=0.55]{./fig/triangles}
\end{center}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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