From 40ca6fd94aedd7eadb312be34c51ce4853ee9b20 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 18 Mar 2021 11:10:57 +0100 Subject: [PATCH] Feat: changement de l'exercice 2 --- TST_sti2d/DS/DS_21_03_18/DS_21_03_18.pdf | Bin 176533 -> 109557 bytes TST_sti2d/DS/DS_21_03_18/DS_21_03_18.tex | 132 +++++++++++++---------- 2 files changed, 77 insertions(+), 55 deletions(-) diff --git a/TST_sti2d/DS/DS_21_03_18/DS_21_03_18.pdf b/TST_sti2d/DS/DS_21_03_18/DS_21_03_18.pdf index 10530a0000b5a82d7e98c67d2ecfd23e3fda790e..b46a2a42e0500883022c314480d1653a0645e25b 100644 GIT binary patch delta 63153 zcmV)gK%~Ew;|lfH2Czm31T!)=Gm~KiD1X&kNt4^g6~51}z)fIDZ1ui4l|y1luGpz^ zV$DtR0U|LH5^xbgPNe+$yj}owgAG#B$d*%c00=a?U%&Ugy$2U>3taqggQr(SxWTNz zNN_>mqA3%sIKbQdn_qso`Rnb?(-*=N6eB6AC~ofxsuAO|P{tsxX>q$QUX{;YE`OF( zky0&wz5Ov-P$&i= zHc%ILH~)-Q#Z++tQ&K{dotg>_gt}GpucD0_WF(bgpP1=FDFL*Gecmnz#$|ojG~24J z{hnXm{*6BKx34Lc{*GvW-BgFp-+xg|Ny43{FC>eWBLaw_#gY(Ygz(G#eL+QOm*Kd4 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zoH0D?V|fyq$1jwLU~(CcEwBzBrz<>I3v8|aPG(TXy|zEfdr*|JKj;YGdV_ldEBNCJ ziK)1E?jdZL-mYo%eq(AoH{msS3nZ2e1mRL_I9{(DchKl7 zmSNSOEc}wnad%KbB;3!LTllT{+6~rJ#+dPcz)P$wL`+2gkqzWa87&3-31Vf{gJV>& z^fV=6X8pp5G>CMViCBr4zmfnuJLj(?(^owJj#1jy%|@JAaAC|vS8PaXa{Ro-tqr9^Nmod?=ulgu{+idZgGR}N!r>Da)upkBYED8=nx zfXPpN-xmXq?99xaR4pC;RPvBt*b*kmEMw?RXqZQ}ilg^)v?C%D<-LDb&*IRXh1wW^ zBQHxsT&#apa>BU0c0tzbH))ZqxaPa{Q$<`8SB_xmJ0#BI@#3F_P};c&z-j1Qwihj6)KM?x;Kb%Fd3U+?z1|#VDx!J3!W8VVr$B^#yIsZr|U)`n!0b>IMjzi9_ ze?b32!8H7NTPNs5;gbBGm|+huvBRqFIt9ckDP$rn3o@HQ=7dfg9{ zDf@UxPww))^Q5wQd-5c^(C9QPNC;mtKH17%st`GBUP22p8a*o&IT-;e, very thick] (-5, 0) -- (5, 0); +% \draw [->, very thick] (0, -5) -- (0, 5); +% %\tkzAxeXY +% \foreach \x in {0,1,...,5} { +% % dots at each point +% \draw[black] (0, 0) circle(\x); +% } +% \end{tikzpicture} +% \end{center} +% +% \item Donner l'affixe du point B sous forme algébrique et sous forme exponentielle. +% \end{enumerate} +% +% \item L'extrémité B du bras peut-elle atteindre un objet qui se trouve à une distance de $4,5$ +% unités du point O? +% \item Pour soulever un objet lourd dont le point d'accroche est le point C (voir figure ci-contre), il faut rigidifier l'articulation en A. On décide alors de bloquer l'angle $\left ( \vec{AO}~,~\vec{AB}\right )$ tel qu'une mesure de cet angle soit constamment égale à $\dfrac{\pi}{2}$ radians. +% +% \hfill +% \includegraphics[scale=0.25]{./fig/bras2} +% \hfill{} +% +% \begin{enumerate} +% \item Déterminer la longueur OB. +% \item Le point C a pour affixe $z_{\text C} = 2\sqrt{2}\e^{i\frac{\pi}{12}}$. +% +% Justifier que l'extrémité B du bras articulé pourra atteindre le point d'accroche C de l'objet. +% +% \item Lorsque le bras articulé saisit l'objet, les points B et C sont confondus. +% +% Calculer la mesure de l'angle que forme alors le bras [OA] avec l'axe [O$x$). +% \end{enumerate} +% \end{enumerate} +% \end{exercise} - Deux exemples de position du bras articulé sont donnés ci-dessous à titre indicatif. - - \begin{center} - \includegraphics[scale=0.25]{./fig/bras1} - \end{center} - - \begin{enumerate} - \item - \begin{enumerate} - \item Sur le repère orthonormé \Ouv ci-dessous, placer le point A d'affixe $z_{\text A}= 2i$ puis construire l'extrémité B du bras articulé lorsque son affixe $z_{\text B}$ a pour argument $\dfrac{\pi}{4}$. - - \begin{center} - \begin{tikzpicture}[baseline=(a.north), xscale=0.6, yscale=0.6] - \tkzInit[xmin=-5,xmax=5,xstep=1, - ymin=-5,ymax=5,ystep=1] - \tkzGrid - \draw (1, 0) node [below right] {1}; - \draw (0, 1) node [above left] {$i$}; - \draw [->, very thick] (-5, 0) -- (5, 0); - \draw [->, very thick] (0, -5) -- (0, 5); - %\tkzAxeXY - \foreach \x in {0,1,...,5} { - % dots at each point - \draw[black] (0, 0) circle(\x); - } - \end{tikzpicture} - \end{center} - - \item Donner l'affixe du point B sous forme algébrique et sous forme exponentielle. - \end{enumerate} - - \item L'extrémité B du bras peut-elle atteindre un objet qui se trouve à une distance de $4,5$ - unités du point O? - \item Pour soulever un objet lourd dont le point d'accroche est le point C (voir figure ci-contre), il faut rigidifier l'articulation en A. On décide alors de bloquer l'angle $\left ( \vec{AO}~,~\vec{AB}\right )$ tel qu'une mesure de cet angle soit constamment égale à $\dfrac{\pi}{2}$ radians. - - \hfill - \includegraphics[scale=0.25]{./fig/bras2} - \hfill{} - - \begin{enumerate} - \item Déterminer la longueur OB. - \item Le point C a pour affixe $z_{\text C} = 2\sqrt{2}\e^{i\frac{\pi}{12}}$. - - Justifier que l'extrémité B du bras articulé pourra atteindre le point d'accroche C de l'objet. - - \item Lorsque le bras articulé saisit l'objet, les points B et C sont confondus. - - Calculer la mesure de l'angle que forme alors le bras [OA] avec l'axe [O$x$). - \end{enumerate} - \end{enumerate} -\end{exercise}