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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N� 13740957055141--
%%--Devoir sur la trigonom�trie--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%
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%\Date{Le 26 avril 2004}
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\begin{exercise}
$\vspace*{-0.35cm}$

\begin{enumerate}
\item Convertir en degr\'{e}s:

$\dfrac{\pi}{10}%
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\quad;\quad0,25\pi%
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\quad;\quad\dfrac{5\pi}{3}%
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\operatorname{rad}%
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\quad;\quad\pi%
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\quad.$

\item Convertir en radians:

$60%
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\quad;\quad90%
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\quad;\quad120%
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\quad;\quad270%
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\quad;\quad180%
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\quad.$
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\end{exercise}

\begin{exercise}
$\vspace*{-0.35cm}$

\begin{enumerate}
\item Donner le tableau de variation des fonctions $\sin$ et $\cos$ sur
l'intervalle $\left[  -\pi;\pi\right]  $ (un tableau par fonction).

\item
\begin{enumerate}
\item Tracer la courbe d'\'{e}quation $y=\cos x$ dans le rep\`{e}re de la
figure \ref{rep_trig1} page \pageref{rep_trig1}, en faisant bien
appara\^{\i}tre les valeurs de $\cos x$ pour les valeurs de $x$ marqu\'{e}es
sur l'axe des abscisses.

\item M\^{e}me question pour la courbe d'\'{e}quation $y=\sin x$ dans le
rep\`{e}re de la figure \ref{rep_trig2} page \pageref{rep_trig2}.
\end{enumerate}
\end{enumerate}
\end{exercise}

\begin{exercise}
On pose $I=\left[  \pi;2\pi\right]  $.

\begin{enumerate}
\item Quelle est le signe de $\sin x$ pour $x\in I$ ?

R\'{e}soudre dans $I$ l'\'{e}quation $\cos x=\dfrac{\sqrt{3}}{2}.$

\item Sachant que lorsque l'on demande \`{a} une calculatrice de r\'{e}soudre
l'\'{e}quation $\sin x=\dfrac{\sqrt{2-\sqrt{2}}}{2}$ elle renvoie
$x=\dfrac{\pi}{8}$ ;%

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\begin{enumerate}
\item Calculer $\cos\dfrac{\pi}{8}$.

\item R\'{e}soudre $\sin x=\dfrac{\sqrt{2-\sqrt{2}}}{2}$ sur $\left[
\dfrac{\pi}{2};\dfrac{3\pi}{2}\right]  $.
\end{enumerate}%

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\begin{exercise}
Dans chacun des cas suivants, marquer en rouge sur un cercle
trigonom\'{e}trique l'arc de cercle correspondant aux angles de l'intervalle
$I$ puis donner le meilleur encadrement de $\cos x$ et $\sin x$ pour $x\in I$ :%

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\begin{enumerate}
\item $I=\left[  \dfrac{\pi}{3};\dfrac{2\pi}{3}\right]  .$

\item $I=\left[  \dfrac{-\pi}{3};\dfrac{\pi}{6}\right]  .$

\item $I=\left[  \dfrac{\pi}{3};\dfrac{5\pi}{3}\right]  .$

\item $I=\left[  \dfrac{\pi}{4};\dfrac{3\pi}{4}\right]  \cup\left[
-\pi;\dfrac{-\pi}{4}\right]  .$
\end{enumerate}%

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\end{exercise}%

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