From 9b39655d7f2252851f6771e97adb9ca3ba4742f5 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Fri, 26 Sep 2025 11:30:01 +0200 Subject: [PATCH] =?UTF-8?q?feat(1G=5Fmath):=20d=C3=A9but=20du=20cous=20sur?= =?UTF-8?q?=20les=20radians?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 1G_math/03_Radians/1B_radian.pdf | Bin 0 -> 15909 bytes 1G_math/03_Radians/1B_radian.tex | 65 ++++++ 1G_math/03_Radians/2B_mesure_principale.pdf | Bin 0 -> 27717 bytes 1G_math/03_Radians/2B_mesure_principale.tex | 111 ++++++++++ 1G_math/03_Radians/3B_sin_cos.pdf | Bin 0 -> 7234 bytes 1G_math/03_Radians/3B_sin_cos.tex | 17 ++ 1G_math/03_Radians/exercises.tex | 224 ++++++++++++++++++++ 1G_math/03_Radians/index.rst | 54 +++++ 1G_math/03_Radians/plan_de_travail.pdf | Bin 0 -> 42064 bytes 1G_math/03_Radians/plan_de_travail.tex | 54 +++++ 1G_math/03_Radians/solutions.tex | 28 +++ 11 files changed, 553 insertions(+) create mode 100644 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--- /dev/null +++ b/1G_math/03_Radians/1B_radian.tex @@ -0,0 +1,65 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Radians - Cours} +\date{septembre 2025} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\section{Cercle trigonométrique} +\begin{definition}[Cercle trigonométrique] + \begin{minipage}{0.6\textwidth} + Un \textbf{cercle trigonométrique} est un cercle de centre $O$ et de rayon 1 dont le sens de parcours est orienté \textbf{positivement} dans le sens inverse des aiguilles d'une montre. + + On appelle ce sens le sens \textbf{direct} ou \textbf{anti-horaire}. + \end{minipage} + \hfill + \begin{minipage}{0.3\textwidth} + \begin{tikzpicture}[scale=2] + \cercleTrigo + \draw[->, thick, red] (120:1.2) arc (120:150:1.2); + \node[red] at (-1,1) {\huge$+$}; + \draw (0.5,0) node[below] {1}; + \end{tikzpicture} + \end{minipage} +\end{definition} + +\section{Angles en radians} +\begin{definition}[Angle en radians] + \begin{minipage}{0.6\textwidth} + Soit $A$ un point sur un cercle trigonométrique. + + On appelle la mesure en \textbf{radian} de l'angle $\widehat{IOA}$ la longueur de l'arc de cercle entre $I$ et $A$ orienté par le sens trigonométrique. + \end{minipage} + \hfill + \begin{minipage}{0.3\textwidth} + \begin{tikzpicture}[scale=2] + \cercleTrigo + \draw[->, thick] (120:1.2) arc (120:150:1.2); + \node[] at (-1,1) {$+$}; + \draw (0.5,0) node[below] {1}; + + \draw[very thick, red] (0:1) arc (0:45:1); + \draw[->, very thick, red] (0:0.3) arc (0:45:0.3); + \draw[red] (0; 0) -- (45:1) node[above right] {\large$A$}; + + \end{tikzpicture} + \end{minipage} +\end{definition} + +\paragraph{Exemples}: voir la correction de l'exercice 2 du plan de travail. + +\begin{propriete}[Convertion degré - radian] + Les mesures d'angles en radians et en degré sont proportionnelles + + \[ + \mbox{mesure en radian} = \mbox{mesure en degré} \times \frac{\pi}{180} + \] +\end{propriete} + +\end{document} diff --git 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On note aussi $L$ le point qui a pour abscisse −1 sur la droite $(I K )$. + + \begin{itemize} + \item Si on enroule sur le cercle $\mathcal{C}$, la demi-droite $[I K )$ des réels positifs dans le sens direct et la demi-droite $[I L)$ des réels négatifs dans le sens indirect, à tout réel $x$ correspond un unique point $M$ du cercle $\mathcal{C}$ , appelé \textbf{image de x sur le cercle $\mathcal{C}$}. + \item Réciproquement, tout point $M$ du cercle $\mathcal{C}$ est l’image d’une infinité de points de la droite $(I J )$. Si $M$ est l’image du réel $x$ alors $M$ est l’image de tous les réels $x + k2\pi$ avec $k$ entier relatif et $x$ est une mesure de l'angle $\widehat{IOM}$ en radian. + \end{itemize} + \end{minipage} + \hfill + \begin{minipage}{0.3\textwidth} + \begin{tikzpicture}[scale=2] + \cercleTrigo + \draw[->, thick] (120:1.2) arc (120:150:1.2); + \node[] at (-1,1) {$+$}; + \draw (0.5,0) node[below] {1}; + + % Droite des réels tangente au cercle en I + \draw[thick, blue] (1,-2.2) -- (1,2.2); + \draw (1,0.5) node[right] {1}; + \draw[blue] (1,1) node{\bullet} node[right] {$K$}; + \draw[blue] (1,-1)node{\bullet} node[right] {$L$}; + + % Illustration du dépliement + + \draw[very thick, red] (0:1) arc (0:120:1); + %\draw[->, very thick, red] (0:0.3) arc (0:120:0.3); + \draw[red] (0; 0) -- (120:1) node[above left] {\large$M$}; + \draw[dashed, blue] (120:1) to[bend left=30] (1,2.094) node {\bullet} node[right] {$x$}; + + \draw[very thick, red] (0:1) arc (0:-120:1); + %\draw[->, very thick, red] (0:0.3) arc (0:-60:0.3); + \draw[red] (0; 0) -- (-120:1) node[below left] {\large$M'$}; + \draw[dashed, blue] (-120:1) to[bend right=30] (1,-2.094) node {\bullet} node[right] {$x'$}; + + \end{tikzpicture} + \end{minipage} +\end{propriete} + +\paragraph{Visualisation de l'enroulement} + + \hfill + \qrcode{https://www.geogebra.org/classic/vctetuhd} + \hfill + \qrcode{https://www.geogebra.org/classic/vhwjvst5} + \hfill + +\begin{definition}[Mesure principale] + On appelle \textbf{mesure principale} de angle en radian $\widehat{IOM}$, le réel $x$ appartenant à $\intOF{-\pi}{\pi}$ dont l'image est $M$. +\end{definition} + +\paragraph{Exemple:} Mesure principale des angles + +\begin{minipage}{0.6\textwidth} + \begin{itemize} + \item $\dfrac{7\pi}{6}$ : + \vspace{1cm} + \item $-\dfrac{5\pi}{3}$ : + \vspace{1cm} + \item $\dfrac{11\pi}{4}$ : + \vspace{1cm} + \end{itemize} + \afaire{} +\end{minipage} + \begin{minipage}{0.4\textwidth} + \begin{center} + \begin{tikzpicture}[scale=3] + \cercleTrigo + + \draw (0,0) -- (30:1) node[above right] {$A$}; + \draw[dashed] (0,0) -- (45:1) node[above right] {$B$}; + \draw (0,0) -- (60:1) node[above right] {$C$}; + + + \draw (0,0) -- (120:1) node[above left] {$D$}; + \draw[dashed] (0,0) -- (135:1) node[above left] {$E$}; + \draw (0,0) -- (150:1) node[above left] {$F$}; + + \draw[dashed] (0,0) -- (180:1) node[below left] {$G$}; + + \draw (0,0) -- (-30:1) node[below right] {$F$}; + \draw[dashed] (0,0) -- (-45:1) node[below right] {$G$}; + \draw (0,0) -- (-60:1) node[below right] {$H$}; + + \draw (0,0) -- (-120:1) node[below left] {$K$}; + \draw[dashed] (0,0) -- (-135:1) node[below left] {$L$}; + \draw (0,0) -- (-150:1) node[below left] {$M$}; + \end{tikzpicture} + \end{center} + \end{minipage} + +\end{document} diff --git a/1G_math/03_Radians/3B_sin_cos.pdf b/1G_math/03_Radians/3B_sin_cos.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9b428dc937c649d5002dfc96e257366feb4aaff1 GIT binary patch literal 7234 zcmcgxcT`hLw+BR!AXPv*p-Cr&BvdKVdq;W?5LzH4bdWAe2N49MqjW?N1Vlx8Rgt1p zrAiTyBGTlAd++yjt?#b;-ap>6a?Y7GvokaM>^-~uHm{zNiU>qh9Kbs;+BVYp{!K?0 z00smD(e|zY85tnRD8LH|1exmEyCNO1K#(EM9{Wd+3L4`91f4zqpnw2D*RG-cffo3` zf`Jh5pSKkdq-}@Apw9Xse~$d|#P=H@eb6|J1JVZw$9Eavr$V`7kr@2j-42UXLOP%w z@#|_KJ)N;GKnNTtD+~P31@OUQkaivb|A}{0Lwfu}ABhM^PYAaFNKePVM)0k({fpyg z{`dHh_-%Yh{;PaI&LsGI1Ohozf`3mU5a{pYbsv{w7Wk|1KwI%KUpc5&M;se=_l6;9qV0PZN(b=yz=gQ$Jf1`bJu~VVGLLXh2IE z==Qa0*C;C&_7@!uSU&?0`5j%hqPA0J-Q4 zhzy0~IR~v<33f81=&htMO*(D84KhfY zxqX)vx)+jIBQ$(BjbZst6px6veXA8_q8oB7yFE~{LlRS?SsIWwSAQN>K6`vfvAoqF zMK4)#pmwDX2eS|emd3Tz(^kY;%@w;<5j)(yD7l=uT}h9-X+~yvy-ZM^a;)jBD$ z{PxtHVc4lcF0U(O8ihy!RyEE*g)1^FW1SeyUhGKX9=PndyMzkoYEQX;K<%ubhAK|H z6RBuV^*}4c&4Z_xhSnISTje;k5^De33BrCo75^jwDD3Z@tb;AU;iGM`?IVlOq;R#D za|8sAlSE;Ev(T?$!~ez!it0)#Xiw}}kN{TvXD<(hL4VPKpDK`Gf-<7J&QSfhteOuy z5vB8~7gFYFS;)_2JCaEQn`8DSB<2MMar4`u4la^cyMBttkK4SDr}#o z{ZVa^@O;^R@xAie$BwP0@ENGL5)T~TL)?AT_cQ4(bCiq+M5)vyQH-((&q_p}THL#gdb4()i-Iz7OyI4$ zz7#s7aOROZM}Y<1<<+OB`SY?RnQdx7r#@QFn&tucL zLdSEsL?%w1kK_`2fN1!AB9T|KHX*gf?Rl;1ze5*{Jt)h(MN`3)Jh_|3le1|QwqQk4tQmeqiCu|c7 zMclU~n!|JoWuEjF4DFs1B+}_hDP-QzG(M?Zh

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Quel est la mesure de l'angle $\widehat{IOA}$? Quelle est le longueur de l'arc de cercle entre $I$ et $A$? + \item Quel est la mesure de l'angle $\widehat{IOJ}$? Quelle est le longueur de l'arc de cercle entre $I$ et $J$? + \item Quel est la mesure de l'angle $\widehat{IOJ}$? Quelle est le longueur de l'arc de cercle entre $I$ et $J$? + \item Placer le point $B$ sur le cercle $\mathcal{C}$ tel que $\widehat{IOB} = 45°$. Quelle est le longueur de l'arc de cercle entre $I$ et $B$? + \item Placer le point $C$ sur le cercle $\mathcal{C}$ tel que $\widehat{IOC} = 60°$. Quelle est le longueur de l'arc de cercle entre $I$ et $C$? + \item Placer le point $D$ sur le cercle $\mathcal{C}$ tel que $\widehat{IOD} = 30°$. Quelle est le longueur de l'arc de cercle entre $I$ et $D$? + \item Compléter le tableau suivant et déterminer un calcul qui permet de convertir un angle en degré en longueur d'arc. + \begin{center} + \begin{tabular}[c]{|l|*{5}{c|}} + \hline + Angle & $\widehat{IOA}$ & $\widehat{IOB}$ & $\widehat{IOC}$ & $\widehat{IOD}$ & Tour entier\\ + \hline + Mesure en degré & & & & & \\ + \hline + Longueur de l'arc & & & & & \\ + \hline + \end{tabular} + \end{center} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Placer les angles}, step={2}, origin={http://auriolg.free.fr/sab/1speechs.pdf}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\trainMode}] + \begin{minipage}{0.6\textwidth} + On considère le le cercle trigonométrique ci-contre. + + Les segments en pointillé partagent le cercle en huit angles de 45 et les autres en douze angles de 30°. + + Associer les angles suivants aux points placés sur le cercle trigonométrique. + + \begin{multicols}{3} + \begin{enumerate}[label=\alph*)] + \item $\dfrac{\pi}{6}$ + \item $\dfrac{\pi}{3}$ + \item $\dfrac{2\pi}{3}$ + \item $\dfrac{5\pi}{4}$ + \item $\dfrac{7\pi}{6}$ + + \item $\dfrac{4\pi}{3}$ + \item $\dfrac{5\pi}{3}$ + \item $\dfrac{11\pi}{6}$ + \item $\dfrac{9\pi}{4}$ + \item $\dfrac{7\pi}{2}$ + + \item $\dfrac{-\pi}{3}$ + \item $\dfrac{-\pi}{4}$ + \item $\dfrac{-6\pi}{3}$ + \item $\dfrac{-13\pi}{4}$ + \item $\dfrac{-20\pi}{2}$ + \end{enumerate} + \end{multicols} + \end{minipage} + \begin{minipage}{0.4\textwidth} + \begin{center} + \begin{tikzpicture}[scale=3] + \cercleTrigo + + \draw (0,0) -- (30:1) node[above right] {$A$}; + \draw[dashed] (0,0) -- (45:1) node[above right] {$B$}; + \draw (0,0) -- (60:1) node[above right] {$C$}; + + + \draw (0,0) -- (120:1) node[above left] {$D$}; + \draw[dashed] (0,0) -- (135:1) node[above left] {$E$}; + \draw (0,0) -- (150:1) node[above left] {$F$}; + + \draw[dashed] (0,0) -- (180:1) node[below left] {$G$}; + + \draw (0,0) -- (-30:1) node[below right] {$F$}; + \draw[dashed] (0,0) -- (-45:1) node[below right] {$G$}; + \draw (0,0) -- (-60:1) node[below right] {$H$}; + + \draw (0,0) -- (-120:1) node[below left] {$K$}; + \draw[dashed] (0,0) -- (-135:1) node[below left] {$L$}; + \draw (0,0) -- (-150:1) node[below left] {$M$}; + \end{tikzpicture} + \end{center} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Angles représentant le même point}, step={2}, origin={}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\trainMode}] + \begin{minipage}{0.6\textwidth} + On considère le le cercle trigonométrique ci-contre. On a partager le cercle trigonométrique en 24 segments. + + \begin{enumerate} + \item Quel est la mesure de l'angle $\widehat{IOA}$? + \item Associer entre eux les nombres qui correspondent aux mêmes points sur le cercle. + \begin{multicols}{3} + \begin{enumerate}[label=\alph*)] + \item $\dfrac{8\pi}{3}$ + \item $-\dfrac{11\pi}{6}$ + \item $\dfrac{\pi}{3}$ + + \item $\dfrac{13\pi}{4}$ + \item $\dfrac{2\pi}{3}$ + \item $-\dfrac{5\pi}{3}$ + + \item $\dfrac{\pi}{6}$ + \item $\dfrac{5\pi}{4}$ + \item $-\dfrac{4\pi}{3}$ + + \item $\dfrac{13\pi}{6}$ + \item $\dfrac{7\pi}{3}$ + \item $-\dfrac{3\pi}{4}$ + \end{enumerate} + \end{multicols} + \item Pour chaque "famille", trouver la mesure correspondante dans l'intervalle $\intOF{-\pi}{\pi}$. + \end{enumerate} + + \end{minipage} + \begin{minipage}{0.4\textwidth} + \begin{center} + \begin{tikzpicture}[scale=3] + \cercleTrigo + + % Diviser le cercle en 24 segments égaux + \foreach \angle in {0,15,...,345} { + \draw[thin, gray] (0,0) -- (\angle:1); + } + \draw (15:1) node[right] {$A$} ; + + \end{tikzpicture} + \end{center} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Mesure principale}, step={2}, origin={}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\trainMode}] + Retrouver la mesure principale des angles suivants, vous les placerez ensuite sur un cercle trigonométrique. + + \begin{multicols}{4} + \begin{enumerate}[label=\alph*)] + \item $\dfrac{7\pi}{4}$ + \item $\dfrac{11\pi}{6}$ + \item $\dfrac{9\pi}{4}$ + \item $\dfrac{13\pi}{6}$ + \item $\dfrac{17\pi}{4}$ + \item $-\dfrac{7\pi}{4}$ + \item $-\dfrac{5\pi}{3}$ + \item $-\dfrac{11\pi}{6}$ + \item $-\dfrac{9\pi}{4}$ + \item $-\dfrac{13\pi}{3}$ + \item $\dfrac{19\pi}{6}$ + \item $-\dfrac{15\pi}{4}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Vrai-Faux}, step={3}, origin={}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\trainMode}] + Dire si les propositions suivantes sont vraies ou fausses. Vous justifierez vos réponses par un croquis ou vous trouverez des contre-exemples. + \begin{multicols}{2} + \begin{enumerate} + \item Pour tout réel $x \in \intFF{\frac{-\pi}{2}}{\frac{\pi}{2}}$, $\cos{x} \geq 0$. + \item Pour tout réel $x \in \intFF{0}{\pi}$, $\sin{x} \geq 0$. + \item Pour tout réel $x \in \intFF{0}{\pi}$, $\cos{x} \geq 0$. + \item Pour tout réel $x$, $0 \leq \cos^2{x} \leq 1$. + \item (*) Pour tout réel $x$, $\sin{2x} = 2 \sin{x}$. + \item (*) Pour tout réel $\alpha$, $\cos(\alpha + x) = \sin(\alpha)$. + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Valeurs de $\sin$ et $\cos$ - premier quadrant}, step={3}, origin={}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\trainMode}] + En vous aidant du tableau des valeurs de $\sin$ et de $\cos$ ainsi que du cercle trigonométrique, déterminer les valeurs suivantes + + \begin{multicols}{4} + \begin{enumerate} + \item $\cos\left(\dfrac{\pi}{6}\right)$ + \item $\sin\left(\dfrac{\pi}{4}\right)$ + + \item $\cos\left(\dfrac{\pi}{2}\right)$ + \item $\sin\left(\dfrac{13\pi}{6}\right)$ + + \item $\cos\left(\dfrac{17\pi}{4}\right)$ + \item $\sin\left(\dfrac{\pi}{3}\right)$ + + \item $\cos\left(\dfrac{-5\pi}{3}\right)$ + \item $\sin\left(\dfrac{-6\pi}{4}\right)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Valeurs de $\sin$ et $\cos$}, step={3}, origin={}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\trainMode}] + En vous aidant du tableau des valeurs de $\sin$ et de $\cos$ ainsi que du cercle trigonométrique, déterminer les valeurs suivantes + + \begin{multicols}{4} + \begin{enumerate} + \item $\cos\left(\dfrac{2\pi}{3}\right)$ + \item $\sin\left(\dfrac{3\pi}{4}\right)$ + \item $\cos\left(\pi\right)$ + \item $\sin\left(\dfrac{5\pi}{6}\right)$ + \item $\cos\left(\dfrac{5\pi}{4}\right)$ + \item $\sin\left(\dfrac{4\pi}{3}\right)$ + \item $\cos\left(\dfrac{5\pi}{3}\right)$ + \item $\sin\left(\dfrac{7\pi}{4}\right)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Valeurs de $\cos(\frac{\pi}{4})$ et $\sin(\frac{\pi}{4})$}, step={4}, origin={Classique}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\paperMode}] + Dans cet exercice, on cherche à démontrer que $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ et $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$. + \begin{enumerate} + \item Tracer un cercle trigonométrique dans le repère $(\vec{OI}; \vec{OJ})$. Placer le point $A$ sur le cercle tel que $\widehat{IOA} = \frac{\pi}{4}$. + \item Placer le point $B$ projeté orthogonal du point $A$ sur l'axe des abscisses et le point $C$ projeté orthogonal du point $A$ sur l'axe des ordonnées. Expliquer pourquoi a-t-on $\cos(\frac{\pi}{4}) = OB$ et $\sin(\frac{\pi}{4}) = OC = AB$. + \item Démontrer que le triangle $OAB$ est isocèle rectangle en $B$. + \item En déduire la longueur $OB$. + \item En déduire les valeurs de $\cos{\frac{\pi}{4}}$ et de $\sin{\frac{\pi}{4}}$ + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Valeurs de $\cos(\frac{\pi}{3})$ et $\sin(\frac{\pi}{3})$}, step={4}, origin={Classique}, topics={ Radians }, tags={ trigonométrie, géométrie }, mode={\paperMode}] + Dans cet exercice, on cherche à démontrer que $\cos(\frac{\pi}{3}) = \frac{1}{2}$ et $\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$. + \begin{enumerate} + \item Tracer un cercle trigonométrique dans le repère $(\vec{OI}; \vec{OJ})$. Placer le point $A$ sur le cercle tel que $\widehat{IOA} = \frac{\pi}{4}$. + \item Placer le point $B$ projeté orthogonal du point $A$ sur l'axe des abscisses et le point $C$ projeté orthogonal du point $A$ sur l'axe des ordonnées. Expliquer pourquoi a-t-on $\cos(\frac{\pi}{3}) = OB$ et $\sin(\frac{\pi}{3}) = OC = AB$. + \item Démontrer que le triangle $OAI$ est équilatéral. + \item En déduire la longueur $OB$ puis la valeur de $\cos(\frac{\pi}{3})$. + \item En se plaçant dans le triangle $AOB$, calculer la longueur $AB$ puis en déduire la longueur $\sin(\frac{\pi}{3})$. + \end{enumerate} +\end{exercise} diff --git a/1G_math/03_Radians/index.rst b/1G_math/03_Radians/index.rst new file mode 100644 index 0000000..a6afb1f --- /dev/null +++ b/1G_math/03_Radians/index.rst @@ -0,0 +1,54 @@ +Radians +####### + +:date: 2025-09-29 +:modified: 2025-09-29 +:authors: Benjamin Bertrand +:tags: trigonométrie, géométrie +:category: 1G_math +:summary: Découverte et manipulation des radians + + +Éléments du programme +===================== + +Contenus +-------- + +- Cercle trigonométrique. Longueur d’arc. Radian. +- Enroulement de la droite sur le cercle trigonométrique. Image d’un nombre réel. +- Cosinus et sinus d’un nombre réel. Lien avec le sinus et le cosinus dans un triangle rectangle. Valeurs remarquables. + +Capacités attendues +------------------- + +- Placer un point sur le cercle trigonométrique. +- Lier la représentation graphique des fonctions cosinus et sinus et le cercle trigonométrique. + +Commentaires +------------ + +Progression +=========== + +Étape 1: Découverte du cercle trigo et des radians +-------------------------------------------------- + +Calculs de longueurs d'arc à partir d'angles en degrés. + +Visualisation de l'enroulement de la droite des réels sur le cercle trigonométrique. + +Cours: Définition du cercle trigo, du sens et angles en radian + +Étape 2: Placer des angles en radian et mesure principale d'en angle +-------------------------------------------------------------------- + +Placer des angles sur le cercle trigo. +Trouver la mesure principale d'un angle. + +Cours: définition de la mesure principale d'un angle + +Étape 3: Sinus et cosinus d'un angle +------------------------------------ + +Cours: définition du sinus et du cosinus d'un 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