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Déterminez à l'aide du cercle trigonométrique la valeur de \(\sin\dfrac{4\pi}{3} \).
\( \dfrac{1}{2} \)
\( -\dfrac{1}{2} \)
\( \dfrac{\sqrt{3}}{2} \)
\( -\dfrac{\sqrt{3}}{2} \)
Résolvez l'équation \(\sin x = -1\) .
\(S=\left\{\dfrac{\pi}{2}\right\} \)
\( S=\left\{\dfrac{3\pi}{2}\right\} \)
\( S=\left\{\dfrac{3\pi}{2}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{2}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\(\sin (3\pi +a)= \)
\( \sin a \)
\( -\sin a \)
\( \cos a \)
\( \pi+\sin a \)
\(\sin (2\pi +a)= \)
\(\sin a \)
\(2\pi+\sin a \)
Résolvez l'équation \(tg\, 3x = \dfrac{\sqrt{3}}{3}\) .
\( S=\left\{\dfrac{\pi}{18}\right\} \)
\( S=\left\{\dfrac{\pi}{18}+k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{18}+2k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{18}+2k\pi;\, k\in\mathbb{Z}\right\} \)
Si \(\alpha=53^{\circ}\) , alors l'opposé de \(\alpha\) vaut
\( 35^{\circ} \)
\( 233^{\circ} \)
\( 413^{\circ} \)
\( -53^{\circ} \)
Déterminez à l'aide du cercle trigonométrique la valeur de \(\cos\dfrac{4\pi}{3}\) .
Sans calculatrice, calculez \(\cos\theta\) si \(\theta=315^{\circ}\) .
\( \dfrac{\sqrt{2}}{2} \)
\( \dfrac{7\pi}{4} \)
\( -\dfrac{\sqrt{2}}{2} \)
Résolvez l'équation \(\cos(3x+\pi) = \cos x \).
\( S=\left\{-\dfrac{\pi}{2}+k\pi,\, -\dfrac{\pi}{4}+k\dfrac{\pi}{2};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{-\dfrac{\pi}{2},\, -\dfrac{\pi}{4};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{-\dfrac{\pi}{2}+k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{-\dfrac{\pi}{2}+2k\pi,\, -\dfrac{\pi}{4}+2k\dfrac{\pi}{2};\, k\in\mathbb{Z}\right\} \)
Convertissez en degrés l'angle \(5\pi \over 2 \).
\(90\mbox{ degrés}\)
\(\dfrac{5}{2} \mbox{ degrés}\)
\( \dfrac{1}{4}\mbox{ degrés}\)
\( \dfrac{\pi}{2}\mbox{ degrés}\)
