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Résolvez l'équation \(\cos 2x = \dfrac{\sqrt{2}}{2}\) .
\( S=\left\{\dfrac{\pi}{8}+k\pi,\, -\dfrac{\pi}{8}+k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{8}+2k\pi,\, -\dfrac{\pi}{8}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{4}\right\} \)
\( S=\left\{\dfrac{\pi}{8}\right\} \)
Résolvez l'équation \(tg\, x =1\) .
\(S=\left\{\dfrac{\pi}{4}\right\} \)
\(S=\left\{\dfrac{\pi}{4}+k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{4},\, \dfrac{5\pi}{4}\right\} \)
\( S=\left\{\dfrac{\pi}{4}+2k\pi;\, k\in\mathbb{Z}\right\} \)
Donnez la valeur de \(\cos {3\pi \over 4}\) .
\( -\dfrac{1}{2} \)
\( -\dfrac{\sqrt{2}}{2} \)
\( \dfrac{\sqrt{2}}{2} \)
\( 135 \)
Convertissez en radians l'angle \(345^\circ \).
\(\dfrac{23\pi}{12} \mbox{ radians}\)
\( \dfrac{11\pi}{12} \mbox{ radians}\)
\( \dfrac{\pi}{345} \mbox{ radians}\)
\( 345 \mbox{ radians}\)
Déterminez à l'aide du cercle trigonométrique la valeur de \( \sin\dfrac{3\pi}{4} \).
\( \dfrac{1}{2} \)
Résolvez l'équation \(\sin 5x +1=0 \).
\( S=\left\{-\dfrac{1}{5}\right\} \)
\( S=\left\{\dfrac{3\pi}{10},\, -\dfrac{\pi}{10}\right\} \)
\( S=\left\{\dfrac{3\pi}{10}+2k\pi,\, -\dfrac{\pi}{10}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{3\pi}{10}+2k\dfrac{\pi}{5};\, k\in\mathbb{Z}\right\} \)
Déterminez à l'aide du cercle trigonométrique la valeur de \(\sin\dfrac{2\pi}{3} \).
\( \dfrac{\sqrt{3}}{2} \)
\( -\dfrac{\sqrt{3}}{2} \)
Si \(\alpha=53^{\circ}\) , alors l'opposé de \(\alpha\) vaut
\( 35^{\circ} \)
\( 233^{\circ} \)
\( 413^{\circ} \)
\( -53^{\circ} \)
Convertissez en radians l'angle \(-160^\circ \).
\( -160\mbox{ radians}\)
\( \dfrac{8\pi}{9} \mbox{ radians}\)
\(\dfrac{10\pi}{9} \mbox{ radians}\)
\( -\dfrac{10\pi}{9}\mbox{ radians}\)
Sans calculatrice, calculez \(tg\, \theta\) si \(\theta=\dfrac{5\pi}{6}\) .
\( -\dfrac{\sqrt{3}}{3} \)
\( -\sqrt{3} \)
\( \dfrac{\sqrt{3}}{3} \)
\( 150 \)
