Introduction - Fonctions trigonométriques

Introduction - Fonctions trigonométriques#

Exercice 1#

Complétez le tableau et représentez graphiquement la fonction \(\sin(x)\).

\(x\) 0 \(\dfrac{\pi}{6}\) \(\dfrac{\pi}{4}\) \(\dfrac{\pi}{3}\) \(\dfrac{\pi}{2}\) \(\dfrac{2\pi}{3}\) \(\dfrac{3\pi}{4}\) \(\dfrac{5\pi}{6}\) \(\pi\) \(\dfrac{7\pi}{6}\) \(\dfrac{4\pi}{3}\) \(\dfrac{3\pi}{2}\) \(\dfrac{5\pi}{3}\) \(\dfrac{11\pi}{6}\)
\(\sin(x)\)

Solution

\(x\) 0 \(\dfrac{\pi}{6}\) \(\dfrac{\pi}{4}\) \(\dfrac{\pi}{3}\) \(\dfrac{\pi}{2}\) \(\dfrac{2\pi}{3}\) \(\dfrac{3\pi}{4}\) \(\dfrac{5\pi}{6}\) \(\pi\) \(\dfrac{7\pi}{6}\) \(\dfrac{4\pi}{3}\) \(\dfrac{3\pi}{2}\) \(\dfrac{5\pi}{3}\) \(\dfrac{11\pi}{6}\)
\(\sin(x)\) \(0\) \(\dfrac{1}{2}\) \(\dfrac{\sqrt{2}}{2}\) \(\dfrac{\sqrt{3}}{2}\) \(1\) \(\dfrac{\sqrt{3}}{2}\) \(\dfrac{\sqrt{2}}{2}\) \(\dfrac{1}{2}\) \(0\) \(-\dfrac{1}{2}\) \(-\dfrac{\sqrt{3}}{2}\) \(-1\) \(-\dfrac{\sqrt{3}}{2}\) \(-\dfrac{1}{2}\)

Exercice 2#

Complétez le tableau et représentez graphiquement la fonction \(\cos(x)\).

\(x\) 0 \(\dfrac{\pi}{6}\) \(\dfrac{\pi}{4}\) \(\dfrac{\pi}{3}\) \(\dfrac{\pi}{2}\) \(\dfrac{2\pi}{3}\) \(\dfrac{3\pi}{4}\) \(\dfrac{5\pi}{6}\) \(\pi\) \(\dfrac{7\pi}{6}\) \(\dfrac{4\pi}{3}\) \(\dfrac{3\pi}{2}\) \(\dfrac{5\pi}{3}\) \(\dfrac{11\pi}{6}\)
\(\cos(x)\)

Solution

\(x\) 0 \(\dfrac{\pi}{6}\) \(\dfrac{\pi}{4}\) \(\dfrac{\pi}{3}\) \(\dfrac{\pi}{2}\) \(\dfrac{2\pi}{3}\) \(\dfrac{3\pi}{4}\) \(\dfrac{5\pi}{6}\) \(\pi\) \(\dfrac{7\pi}{6}\) \(\dfrac{4\pi}{3}\) \(\dfrac{3\pi}{2}\) \(\dfrac{5\pi}{3}\) \(\dfrac{11\pi}{6}\)
\(\cos(x)\) \(1\) \(\dfrac{\sqrt{3}}{2}\) \(\dfrac{\sqrt{2}}{2}\) \(\dfrac{1}{2}\) \(0\) \(-\dfrac{1}{2}\) \(-\dfrac{\sqrt{2}}{2}\) \(-\dfrac{\sqrt{3}}{2}\) \(-1\) \(-\dfrac{\sqrt{3}}{2}\) \(-\dfrac{1}{2}\) \(0\) \(\dfrac{1}{2}\) \(\dfrac{\sqrt{3}}{2}\)

Exercice 3#

Qu'est-ce qui est semblable et qu'est-ce qui est différent entre la représentation graphique de \(/sin(x)\) et de \(/cos(x)\)

Solution

Les deux fonctions ont la même forme, elles sont juste décalées de \(\dfrac{\pi}{2}\).

Exercice 4#

Complétez le tableau et représentez graphiquement la fonction \(\tan(x)\).

\(x\) 0 \(\dfrac{\pi}{6}\) \(\dfrac{\pi}{4}\) \(\dfrac{\pi}{3}\) \(\dfrac{\pi}{2}\) \(\dfrac{2\pi}{3}\) \(\dfrac{3\pi}{4}\) \(\dfrac{5\pi}{6}\) \(\pi\) \(\dfrac{7\pi}{6}\) \(\dfrac{4\pi}{3}\) \(\dfrac{3\pi}{2}\) \(\dfrac{5\pi}{3}\) \(\dfrac{11\pi}{6}\)
\(\tan(x)\)

Solution

\(x\) 0 \(\dfrac{\pi}{6}\) \(\dfrac{\pi}{4}\) \(\dfrac{\pi}{3}\) \(\dfrac{\pi}{2}\) \(\dfrac{2\pi}{3}\) \(\dfrac{3\pi}{4}\) \(\dfrac{5\pi}{6}\) \(\pi\) \(\dfrac{7\pi}{6}\) \(\dfrac{4\pi}{3}\) \(\dfrac{3\pi}{2}\) \(\dfrac{5\pi}{3}\) \(\dfrac{11\pi}{6}\)
\(\tan(x)\) \(0\) \(\dfrac{\sqrt{3}}{3}\) \(1\) \(\sqrt{3}\) - \(-\sqrt{3}\) \(-1\) \(-\dfrac{\sqrt{3}}{3}\) \(0\) \(\dfrac{\sqrt{3}}{3}\) \(\sqrt{3}\) - \(-\sqrt{3}\) \(-\dfrac{\sqrt{3}}{3}\)