Devoir Surveillé 1 S02 Calcul Trigonométrique E - F
📅 April 23, 2024 | 👁️ Views: 210
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\noindent\begin{tabularx}{\textwidth}{@{} lCr @{}}
Lycee Taghzirt\textbf{/}Prof MOSAID &
2022-2023\textbf{/Devoir 1 S02}\ccc{A}&
TCSF\textbf{/}2h\\
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\exe{1}(4.5pts)\\
\noindent
\begin{tabular}{@{}>{\hfill}r|p{0.96\textwidth}@{}}
&Soit le polynome \(P(x)=x^3+2x^2-5x-6\)\\
\phantom{\(\times 33\)}0.5&\mylabel[green]{1} Montrer que \(P(x)\) est divisible par \(x-2\)\\
3&\mylabel[green]{2} Ecrir \(P(x)\) sous forme de produit de binomes\\
1&\mylabel[green]{3} Résoudre \(x\in \mathbb{R}\quad P(x) < 0\)\\
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\\
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\phantom{1.}\(1\times4\)&\mylabel[green]{1} Soit la figure si contre, donner les mesures :
\((\overline{\overrightarrow{BA},\overrightarrow{BC}})\);
\((\overline{\overrightarrow{CA},\overrightarrow{CB}})\);
\((\overline{\overrightarrow{DC},\overrightarrow{DB}})\);
\((\overline{\overrightarrow{AB},\overrightarrow{AC}})\)\\
1& \mylabel[green]{2} Vérifier que \(\frac{45\pi}{4}\) et \(\frac{-3\pi}{4}\)
Sont des abscisses curvilignes du même point.\\
&\hspace*{0.5cm} Puis le placer sur le cercle trigonométrique\\
2& \mylabel[green]{3} Simplifier:
\(A= 2\cos x +3\cos(\pi+x) +6\sin(\frac{\pi}{2}-x)\)\\
1.5&\mylabel[green]{4} Calculer:
\(B= \sin^2\frac{\pi}{12} + \sin^2\frac{3\pi}{12}+\sin^2\frac{5\pi}{12}\)\\
\end{tabular}
\\
\exe{3}(7pts)\\
\noindent
\begin{tabular}{@{}>{\hfill}r|p{0.96\textwidth}@{}}
\phantom{.5}\(2 \times 2\)&\mylabel[green]{1} Résoudre \(x\in \mathbb{R} \quad \sin(3x- \frac{2\pi}{5}) = 0 \quad\)
et \(\quad x\in [0,2\pi]\quad \cos 3x+\cos 7x = 0\)\\
3&\mylabel[green]{2} Résoudre \(x\in [0,2\pi]\quad \cos x\cdot\sin x < 0\)\\
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%===========================================================================
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Lycee Taghzirt\textbf{/}Prof MOSAID &
2022-2023\textbf{/Devoir 1 S02}\ccc{B}&
TCSF\textbf{/}2h\\
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\exe{1}(2pts)\\
\noindent
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1+1&Résoudre dans \(\mathbb{R}\): \(x^2-3x+6=0\quad\) ; \(\quad 3x^2+4x+5<0\)\\
\end{tabular}
\\
\exe{2}(9pts)\\
\noindent
\begin{tabular}{@{}>{\hfill}r|p{0.96\textwidth}@{}}
\phantom{1+}1&\mylabel[green]{1} Placer le point \(A\left(\frac{197\pi}{4}\right)\),
sur le cercle trigonométrique\\
1& \mylabel[green]{2} Construir un triangle réctangle isocèle \(ABC\) tel que
\(\overline{(\overrightarrow{AB},\overrightarrow{AC})}\equiv \frac{\pi}{2}[2\pi]\)\\
2& \mylabel[green]{3} Sachant \phantom{aa} que \phantom{aa} \(\sin \frac{7\pi}{8} = \frac{\sqrt{2-\sqrt2}}{2}\).
Determiner \(\cos \frac{7\pi}{8}\) et \(\sin \frac{\pi}{8}\)\\
3&\mylabel[green]{4} Simplifer
\(A=\sin\left(15\pi-x\right)\cdot\cos\left(\frac{5\pi}{2}-x\right)-\sin\left(\frac{5\pi}{2}-x\right)\cdot\cos\left(3\pi-x\right)\)\\
2& \mylabel[green]{5} Calculer
\(B=\cos^2 \frac{\pi}{8}+\cos^2 \frac{3\pi}{8}+\cos^2 \frac{5\pi}{8}+\cos^2 \frac{7\pi}{8}\)\\
\end{tabular}
\\
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\noindent
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2+2&\mylabel[green]{1} Résoudre \(x\in [0,2\pi]\quad 2\sin x+\sqrt3 = 0\) et \(x\in [0,2\pi]\quad 2\cos x-\sqrt3 = 0\)\\
3&\mylabel[green]{2} Résoudre \(x\in [0,2\pi]\quad (2\sin x+\sqrt3)(2\cos x-\sqrt3) \le 0\)\\
2&\mylabel[green]{3}Résoudre dans \(\mathbb{R}\quad\) \(\begin{cases}
\cos x = \cos y\\
3x+2y=\pi
\end{cases}\)
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