Révisions et cercles - exercices supplémentaires

Angles remarquables

Exercice 1

Cochez la bonne réponse.

1. • \(\frac{1}{2}\)

   • \(\frac{\sqrt{2}}{2}\)

   • \(\frac{\sqrt{3}}{2}\)

   \(\sin(30^\circ) =\)

2. • \(\frac{\sqrt{3}}{3}\)

   • \(1\)

   • \(\sqrt{3}\)

   \(\tan(45^\circ) =\)

3. • \(\frac{1}{2}\)

   • \(\frac{\sqrt{2}}{2}\)

   • \(\frac{\sqrt{3}}{2}\)

   \(\cos(60^\circ) =\)

4. • \(\frac{1}{2}\)

   • \(\frac{\sqrt{2}}{2}\)

   • \(\frac{\sqrt{3}}{2}\)

   \(\sin(45^\circ) =\)

5. • \(\frac{\sqrt{3}}{2}\)

   • \(\frac{\sqrt{3}}{3}\)

   • \(\sqrt{3}\)

   \(\tan(30^\circ) =\)

6. • \(\frac{1}{2}\)

   • \(\frac{\sqrt{2}}{2}\)

   • \(\frac{\sqrt{3}}{2}\)

   \(\cos(30^\circ) =\)

7. • \(\frac{\sqrt{2}}{2}\)

   • \(\frac{\sqrt{3}}{3}\)

   • \(\frac{\sqrt{3}}{2}\)

   \(\sin(60^\circ) =\)

8. • \(1\)

   • \(\frac{\sqrt{3}}{3}\)

   • \(\sqrt{3}\)

   \(\tan(60^\circ) =\)

9. • \(\frac{1}{2}\)

   • \(\frac{\sqrt{2}}{2}\)

   • \(\frac{\sqrt{3}}{2}\)

   \(\cos(45^\circ) =\)

Angles

Exercice 2

Cochez la bonne réponse.

1. • \(\frac{\pi}{6}\)

   • \(\frac{\pi}{4}\)

   • \(\frac{\pi}{3}\)

   \(45^\circ=\)

2. • \(\frac{\pi}{6}\)

   • \(\frac{\pi}{4}\)

   • \(\frac{\pi}{3}\)

   \(30^\circ=\)

3. • \(\frac{\pi}{6}\)

   • \(\frac{\pi}{4}\)

   • \(\frac{\pi}{3}\)

   \(60^\circ=\)

4. • \(\frac{\pi}{2}\)

   • \(\frac{\pi}{4}\)

   • \(\pi\)

   \(90^\circ=\)

5. • \(\pi\)

   • \(\frac{3\pi}{2}\)

   • \(2\pi\)

   \(180^\circ=\)

6. • \(\pi\)

   • \(\frac{3\pi}{2}\)

   • \(2\pi\)

   \(360^\circ=\)

7. • \(\pi\)

   • \(\frac{3\pi}{2}\)

   • \(2\pi\)

   \(270^\circ=\)

Exercice 3

Cochez la bonne réponse.

1. • \(45^\circ\)

   • \(30^\circ\)

   • \(60^\circ\)

   \(\frac{\pi}{6}=\)

2. • \(90^\circ\)

   • \(360^\circ\)

   • \(180^\circ\)

   \(\pi\)

3. • \(45^\circ\)

   • \(30^\circ\)

   • \(90^\circ\)

   \(\frac{\pi}{4}=\)

4. • \(270^\circ\)

   • \(360^\circ\)

   • \(300^\circ\)

   \(2\pi\)

5. • \(45^\circ\)

   • \(30^\circ\)

   • \(60^\circ\)

   \(\frac{\pi}{3}=\)

6. • \(270^\circ\)

   • \(360^\circ\)

   • \(120^\circ\)

   \(\frac{3\pi}{2}=\)

7. • \(45^\circ\)

   • \(120^\circ\)

   • \(135^\circ\)

   \(\frac{3\pi}{4}=\)

8. • \(270^\circ\)

   • \(120^\circ\)

   • \(135^\circ\)

   \(\frac{2\pi}{3}=\)

9. • \(30^\circ\)

   • \(300^\circ\)

   • \(150^\circ\)

   \(\frac{5\pi}{6}=\)

Équations et cercle trigonométrique

Exercice 4

En vous aidant du cercle trigonométrique, cochez les bonnes réponses.

1. • \(x = 30^\circ\)

   • \(x = 45^\circ\)

   • \(x = \frac{\pi}{6}\)

   \(\sin(x) = \frac{1}{2}\)

2. • \(x = 45^\circ\)

   • \(x = \frac{\sqrt{2}}{2}\)

   • \(x = \sin(\frac{\pi}{4})\)

   \(\cos(\frac{\pi}{4}) = x\)

3. • \(x = 30^\circ\)

   • \(x = 60^\circ\)

   • \(x = 240^\circ\)

   \(\tan(x) = \sqrt{3}\)

4. • \(x = 1\)

   • \(x = 0\)

   • \(x = 2\pi\)

   \(\sin(x) = 0\)

5. • \(x = 45^\circ\)

   • \(x = 45^\circ + 180^\circ\)

   • \(x = \frac{\pi}{4} + 2\pi\)

   \(\cos(x) = \frac{\sqrt{2}}{2}\)

6. • \(x = \frac{\pi}{6}\)

   • \(x = 30^\circ\)

   • \(x = 210^\circ\)

   \(\tan(x) = \frac{\sqrt{3}}{3}\)

7. • \(x = 45^\circ\)

   • \(x = -60^\circ\)

   • \(x = 300^\circ\)

   \(\sin(x) = -\frac{\sqrt{3}}{2}\)

8. • \(x = 1\)

   • \(x = 2\pi\)

   • \(x = 0\)

   \(\cos(x) = 0\)

9. • \(x = 225^\circ\)

   • \(x = 45^\circ\)

   • \(x = 315^\circ\)

   \(\tan(x) = -1\)