\nbPointsRegular{3}\textbf{Associer} chacune des fonctions suivantes
avec son graphe~:

$$a(x) = 4\sin\left( \frac{x}{2} \right), \quad b(x) = 2\sin(2x) + 2 \quad \text{ et }
\quad c(x) = 2\sin\left( \frac{1}{2}\left( x + \frac{\pi}{4} \right) \right).$$

{\begin{center}
\begin{tabularx}{\linewidth}{|*{2}{>{\centering \arraybackslash}X|}}\hline
\ifpdf
\includegraphics[width=6.5cm]{S6P3/2023_June/2023_06_S6P3_EEB1_FR_TestB_ExoA3_IMG1.jpg}
\else
\psset{unit=.5cm}
\def\xMin{-4}
\def\xMax{10}
\def\yMin{-5}
\def\yMax{5}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\pgfmathtruncatemacro{\nbXLines}{(\xMax-\xMin)+1}
\pgfmathtruncatemacro{\nbYLines}{(\yMax-\yMin)+1}
\multido{\n=\xMin+1}{\nbXLines}{\psline[linewidth=0.25pt,linecolor=gray](\n,\yMin)(\n,\yMax)}
\multido{\n=\yMin+1}{\nbYLines}{\psline[linewidth=0.25pt,linecolor=gray](\xMin,\n)(\xMax,\n)}
\psaxes[linewidth=1.5pt,labels=y]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[d](-4,-0.3){$-\pi$}
\uput[d](-2,-0.3){$-\dfrac{\pi}{2}$}
\uput[d](2,-0.3){$\dfrac{\pi}{2}$}
\uput[d](4,-0.3){$\pi$}
\uput[d](6,-0.3){$\dfrac{3\pi}{2}$}
\uput[d](8,-0.3){$2\pi$}
\uput[dl](\xMax,0){$x$} \uput[dr](0,\yMax){$y$}
\psclip{\psframe[linestyle=none](\xMin,\yMin)(\xMax,\yMax)}%
    %changement de variable : 1 <=> pi / 4 donc sin(2(x+pi/2)) correspond à sin(2*(pi/4*x+pi/2))
    \psplot[algebraic,linewidth=1.5pt,linecolor=red,plotpoints=5000]{\xMin}{\xMax}{2*sin(2*(3.14159265359/4*x+3.14159265359/2))+2}
\endpsclip
\end{pspicture}
\fi
&
\ifpdf
\includegraphics[width=6.5cm]{S6P3/2023_June/2023_06_S6P3_EEB1_FR_TestB_ExoA3_IMG2.jpg}
\else
\psset{unit=.5cm}
\def\xMin{-4}
\def\xMax{10}
\def\yMin{-5}
\def\yMax{5}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\pgfmathtruncatemacro{\nbXLines}{(\xMax-\xMin)+1}
\pgfmathtruncatemacro{\nbYLines}{(\yMax-\yMin)+1}
\multido{\n=\xMin+1}{\nbXLines}{\psline[linewidth=0.25pt,linecolor=gray](\n,\yMin)(\n,\yMax)}
\multido{\n=\yMin+1}{\nbYLines}{\psline[linewidth=0.25pt,linecolor=gray](\xMin,\n)(\xMax,\n)}
\psaxes[linewidth=1.5pt,labels=y]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[d](-4,-0.3){$-\pi$}
\uput[d](-2,-0.3){$-\dfrac{\pi}{2}$}
\uput[d](2,-0.3){$\dfrac{\pi}{2}$}
\uput[d](4,-0.3){$\pi$}
\uput[d](6,-0.3){$\dfrac{3\pi}{2}$}
\uput[d](8,-0.3){$2\pi$}
\uput[dl](\xMax,0){$x$} \uput[dr](0,\yMax){$y$}
\psclip{\psframe[linestyle=none](\xMin,\yMin)(\xMax,\yMax)}%
    %changement de variable : 1 <=> pi / 4 donc sin(1/2(x-pi/2)) correspond à sin(1/4*(pi/4*x-pi/2))
    \psplot[algebraic,linewidth=1.5pt,linecolor=red,plotpoints=5000]{\xMin}{\xMax}{2*sin(1/4*(3.14159265359/4*x-3.14159265359/2))}
\endpsclip
\end{pspicture}
\fi
\\
Graphe A & Graphe B\\ \hline
\end{tabularx}

\medskip

\begin{tabularx}{\linewidth}{|*{2}{>{\centering \arraybackslash}X|}}\hline
\ifpdf
\includegraphics[width=6.5cm]{S6P3/2023_June/2023_06_S6P3_EEB1_FR_TestB_ExoA3_IMG3.jpg}
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\psset{unit=.5cm}
\def\xMin{-4}
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\def\yMin{-5}
\def\yMax{5}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\pgfmathtruncatemacro{\nbXLines}{(\xMax-\xMin)+1}
\pgfmathtruncatemacro{\nbYLines}{(\yMax-\yMin)+1}
\multido{\n=\xMin+1}{\nbXLines}{\psline[linewidth=0.25pt,linecolor=gray](\n,\yMin)(\n,\yMax)}
\multido{\n=\yMin+1}{\nbYLines}{\psline[linewidth=0.25pt,linecolor=gray](\xMin,\n)(\xMax,\n)}
\psaxes[linewidth=1.5pt,labels=y]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[d](-4,-0.3){$-\pi$}
\uput[d](-2,-0.3){$-\dfrac{\pi}{2}$}
\uput[d](2,-0.3){$\dfrac{\pi}{2}$}
\uput[d](4,-0.3){$\pi$}
\uput[d](6,-0.3){$\dfrac{3\pi}{2}$}
\uput[d](8,-0.3){$2\pi$}
\uput[dl](\xMax,0){$x$} \uput[dr](0,\yMax){$y$}
\psclip{\psframe[linestyle=none](\xMin,\yMin)(\xMax,\yMax)}%
    %changement de variable : 1 <=> pi / 4 donc sin(2x) correspond à sin(2*pi/4*x)
    \psplot[algebraic,linewidth=1.5pt,linecolor=red,plotpoints=5000]{\xMin}{\xMax}{2*sin(2*3.14159265359/4*x)+2}
\endpsclip
\end{pspicture}
\fi
&
\ifpdf
\includegraphics[width=6.5cm]{S6P3/2023_June/2023_06_S6P3_EEB1_FR_TestB_ExoA3_IMG4.jpg}
\else
\psset{unit=.5cm}
\def\xMin{-4}
\def\xMax{10}
\def\yMin{-5}
\def\yMax{5}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\pgfmathtruncatemacro{\nbXLines}{(\xMax-\xMin)+1}
\pgfmathtruncatemacro{\nbYLines}{(\yMax-\yMin)+1}
\multido{\n=\xMin+1}{\nbXLines}{\psline[linewidth=0.25pt,linecolor=gray](\n,\yMin)(\n,\yMax)}
\multido{\n=\yMin+1}{\nbYLines}{\psline[linewidth=0.25pt,linecolor=gray](\xMin,\n)(\xMax,\n)}
\psaxes[linewidth=1.5pt,labels=y]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[d](-4,-0.3){$-\pi$}
\uput[d](-2,-0.3){$-\dfrac{\pi}{2}$}
\uput[d](2,-0.3){$\dfrac{\pi}{2}$}
\uput[d](4,-0.3){$\pi$}
\uput[d](6,-0.3){$\dfrac{3\pi}{2}$}
\uput[d](8,-0.3){$2\pi$}
\uput[dl](\xMax,0){$x$} \uput[dr](0,\yMax){$y$}
\psclip{\psframe[linestyle=none](\xMin,\yMin)(\xMax,\yMax)}%
    %changement de variable : 1 <=> pi / 4 donc sin(x/2) correspond à sin(pi/4*x/2)
    \psplot[algebraic,linewidth=1.5pt,linecolor=red,plotpoints=5000]{\xMin}{\xMax}{4*sin(3.14159265359/4*x/2)}
\endpsclip
\end{pspicture}
\fi
\\
Graphe C & Graphe D\\ \hline
\end{tabularx}

\medskip

\begin{tabularx}{\linewidth}{|*{2}{>{\centering \arraybackslash}X|}}\hline
\ifpdf
\includegraphics[width=6.5cm]{S6P3/2023_June/2023_06_S6P3_EEB1_FR_TestB_ExoA3_IMG5.jpg}
\else
\psset{unit=.5cm}
\def\xMin{-4}
\def\xMax{10}
\def\yMin{-5}
\def\yMax{5}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\pgfmathtruncatemacro{\nbXLines}{(\xMax-\xMin)+1}
\pgfmathtruncatemacro{\nbYLines}{(\yMax-\yMin)+1}
\multido{\n=\xMin+1}{\nbXLines}{\psline[linewidth=0.25pt,linecolor=gray](\n,\yMin)(\n,\yMax)}
\multido{\n=\yMin+1}{\nbYLines}{\psline[linewidth=0.25pt,linecolor=gray](\xMin,\n)(\xMax,\n)}
\psaxes[linewidth=1.5pt,labels=y]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[d](-4,-0.3){$-\pi$}
\uput[d](-2,-0.3){$-\dfrac{\pi}{2}$}
\uput[d](2,-0.3){$\dfrac{\pi}{2}$}
\uput[d](4,-0.3){$\pi$}
\uput[d](6,-0.3){$\dfrac{3\pi}{2}$}
\uput[d](8,-0.3){$2\pi$}
\uput[dl](\xMax,0){$x$} \uput[dr](0,\yMax){$y$}
\psclip{\psframe[linestyle=none](\xMin,\yMin)(\xMax,\yMax)}%
    %changement de variable : 1 <=> pi / 4 donc sin(2x) correspond à sin(2*pi/4*x)
    \psplot[algebraic,linewidth=1.5pt,linecolor=red,plotpoints=5000]{\xMin}{\xMax}{4*sin(2*3.14159265359/4*x)}
\endpsclip
\end{pspicture}
\fi
&
\ifpdf
\includegraphics[width=6.5cm]{S6P3/2023_June/2023_06_S6P3_EEB1_FR_TestB_ExoA3_IMG6.jpg}
\else
\psset{unit=.5cm}
\def\xMin{-4}
\def\xMax{10}
\def\yMin{-5}
\def\yMax{5}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\pgfmathtruncatemacro{\nbXLines}{(\xMax-\xMin)+1}
\pgfmathtruncatemacro{\nbYLines}{(\yMax-\yMin)+1}
\multido{\n=\xMin+1}{\nbXLines}{\psline[linewidth=0.25pt,linecolor=gray](\n,\yMin)(\n,\yMax)}
\multido{\n=\yMin+1}{\nbYLines}{\psline[linewidth=0.25pt,linecolor=gray](\xMin,\n)(\xMax,\n)}
\psaxes[linewidth=1.5pt,labels=y]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[d](-4,-0.3){$-\pi$}
\uput[d](-2,-0.3){$-\dfrac{\pi}{2}$}
\uput[d](2,-0.3){$\dfrac{\pi}{2}$}
\uput[d](4,-0.3){$\pi$}
\uput[d](6,-0.3){$\dfrac{3\pi}{2}$}
\uput[d](8,-0.3){$2\pi$}
\uput[dl](\xMax,0){$x$} \uput[dr](0,\yMax){$y$}
\psclip{\psframe[linestyle=none](\xMin,\yMin)(\xMax,\yMax)}%
    %changement de variable : 1 <=> pi / 4 donc sin(1/2(x+pi/4)) correspond à sin(1/4*(pi/4*x+pi/4))
    \psplot[algebraic,linewidth=1.5pt,linecolor=red,plotpoints=5000]{\xMin}{\xMax}{2*sin(1/4*(3.14159265359/4*x+3.14159265359/4))}
\endpsclip
\end{pspicture}
\fi
\\
Graphe E & Graphe F\\ \hline
\end{tabularx}
\end{center}}
