import work from year 2015-2016
This commit is contained in:
Benjamin Bertrand
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86
3e/Geometrie/Trigonometrie/index.rst
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86
3e/Geometrie/Trigonometrie/index.rst
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@@ -0,0 +1,86 @@
|
||||
Notes sur le chapitre de trigonométrie pour les 3e
|
||||
##################################################
|
||||
|
||||
:date: 2016-03-18
|
||||
:modified: 2016-03-14
|
||||
:tags: Trigonometrie, Geometrie
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur la trigonométrie pour les 3e.
|
||||
|
||||
Objectif du programme
|
||||
=====================
|
||||
|
||||
- Connaître les relations entre deux côtés et un angle d'un triangle rectangle
|
||||
- Déterminer à la calculatrice la mesure d'un angle à partir de deux côtés
|
||||
- Déterminer à la calculatrice la longueur d'un côté à partir d'un autre et d'un angle
|
||||
|
||||
Cours
|
||||
=====
|
||||
|
||||
Bilan sur Pythagore et cadre et objectif du chapitre.
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Pythagore:
|
||||
|
||||
2 longueur -> la 3e longueur.
|
||||
|
||||
Trigonométrie:
|
||||
|
||||
2 longueur -> un angle
|
||||
1 longueur et un angle -> les autres longueurs
|
||||
|
||||
Vocabulaire du triangle
|
||||
~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Sur une figure:
|
||||
|
||||
- Angle
|
||||
- Hypoténuse
|
||||
- Opposé
|
||||
- Adjacent
|
||||
|
||||
Formules trigonométriques
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Les formules ainsi que 2 exemples pour le calcul de longueur et d'angle.
|
||||
|
||||
Déroulement
|
||||
===========
|
||||
|
||||
Séance 1
|
||||
~~~~~~~~
|
||||
|
||||
Objectif et vocabulaire du triangle.
|
||||
|
||||
Fiche avec les mesures sud les triangles.
|
||||
|
||||
Séance 2
|
||||
~~~~~~~~
|
||||
|
||||
Cours: les 3 formules
|
||||
|
||||
Calculer une longueur à partir d'un angle et d'une longueur.
|
||||
|
||||
Séance 3
|
||||
~~~~~~~~
|
||||
|
||||
Correction du premier exercice (à finir à la maison).
|
||||
Exercice 2 de la fiche.
|
||||
|
||||
Un exemple de calcul d'un angle.
|
||||
|
||||
|
||||
Séance 4
|
||||
~~~~~~~~
|
||||
|
||||
Calcul d'un angle à partir de deux longueurs.
|
||||
|
||||
Idées situations exercices
|
||||
==========================
|
||||
|
||||
- Longueur de plage recouverte par la marée (Brevet des collèges Nouvelle-Calédonie, 11 décembre 2012)
|
||||
- Profondeur de l'ancre avec du courant
|
||||
- Pente en ski
|
||||
- Triangulation navigation (Brevet Nouvelle-Calédonie, 6 décembre 2011)
|
||||
|
||||
BIN
3e/Geometrie/Trigonometrie/intro_trigo.pdf
Normal file
BIN
3e/Geometrie/Trigonometrie/intro_trigo.pdf
Normal file
Binary file not shown.
88
3e/Geometrie/Trigonometrie/intro_trigo.tex
Normal file
88
3e/Geometrie/Trigonometrie/intro_trigo.tex
Normal file
@@ -0,0 +1,88 @@
|
||||
\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
|
||||
|
||||
% Title Page
|
||||
\titre{Introduction à la trigonométrie}
|
||||
\classe{Troisième}
|
||||
\date{mars 2014}
|
||||
|
||||
\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=0.4]{./fig/triangles}
|
||||
\end{center}
|
||||
|
||||
\begin{Exo}
|
||||
|
||||
\textbf{Avec la figure suivante, calculer la longueur $BA$.}
|
||||
\\[0.3cm]
|
||||
|
||||
\begin{minipage}[h]{0.2\textwidth}
|
||||
\includegraphics[scale=0.15]{./fig/triangleABC}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.8\textwidth}
|
||||
\textit{Questions à se poser}
|
||||
\begin{itemize}
|
||||
\item On connait
|
||||
\begin{center}
|
||||
hypoténuse\hspace{0.5cm} opposé \hspace{0.5cm}adjacent \hspace{0.5cm}angle
|
||||
\end{center}
|
||||
\item On cherche
|
||||
\begin{center}
|
||||
hypoténuse\hspace{0.5cm} opposé \hspace{0.5cm}adjacent \hspace{0.5cm}angle
|
||||
\end{center}
|
||||
\end{itemize}
|
||||
\begin{itemize}
|
||||
\item On utilise la formule
|
||||
\begin{eqnarray*}
|
||||
\cos( \widehat{BAC}) = \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.5cm}
|
||||
\sin( \widehat{BAC}) = \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.5cm}
|
||||
\tan( \widehat{BAC}) = \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
\textit{Rédaction:}
|
||||
|
||||
\noindent\fbox{\parbox{\linewidth-2\fboxrule-2\fboxsep}{
|
||||
.\\
|
||||
\parbox{1cm}{\dotfill} est un triangle rectangle en \parbox{0.5cm}{\dotfill} donc
|
||||
\begin{eqnarray*}
|
||||
\parbox{1cm}{\dotfill}(\widehat{BAC}) &=& \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.7cm} \textit{(avec les lettres)}\\[0.3cm]
|
||||
\parbox{1cm}{\dotfill}(\parbox{1cm}{\dotfill}) &=& \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.7cm} \textit{(avec les chiffres)} \\[0.3cm]
|
||||
\parbox{1cm}{\dotfill} &=& \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.7cm} \textit{(avec les chiffres)} \\[0.3cm]
|
||||
BA & = & \parbox{1cm}{\dotfill} \times \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
Donc $BA = \parbox{1cm}{\dotfill}$
|
||||
}}
|
||||
\end{Exo}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Reference in New Issue
Block a user