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Looking for an English version of this section?
This section is in French because the contents are in French. If you prefer the English version of this section, click on the link below.
However, the contents in the French and the English sections are not necessarily the same!• Contents for mathematics in English •
However, the contents in the French and the English sections are not necessarily the same!
Définition de base des fonctions trigonométriques
La fonction cosinus
Valeurs particulières de la fonction cosinus (cos) :
\(\displaystyle cos(0^{\circ})=cos(0)=1\)
\(\displaystyle cos(30^{\circ})=cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}\)
\(\displaystyle cos(45^{\circ})=cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\)
\(\displaystyle cos(60^{\circ})=cos(\frac{\pi}{3})=\frac{1}{2}\)
\(\displaystyle cos(90^{\circ})=cos(\frac{\pi}{2})=0\)
\(\displaystyle cos(x + 2\pi)=cos(x)\)
La fonction sinus
Valeurs particulières de la fonction sinus (sin) :
\(\displaystyle sin(0^{\circ})=sin(0)=0\)
\(\displaystyle sin(30^{\circ})=sin(\frac{\pi}{6})=\frac{1}{2}\)
\(\displaystyle sin(45^{\circ})=sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\)
\(\displaystyle sin(60^{\circ})=sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}\)
\(\displaystyle sin(90^{\circ})=sin(\frac{\pi}{2})=1\)
\(\displaystyle sin(x + 2\pi)=sin(x)\)
La fonction tangente
Valeurs particulières de la fonction tangente (tan) :
\(\displaystyle tan(0^{\circ})=tan(0)=0\)
\(\displaystyle tan(30^{\circ})=tan(\frac{\pi}{6})=\frac{\sqrt{3}}{3}\)
\(\displaystyle tan(45^{\circ})=tan(\frac{\pi}{4})=1\)
\(\displaystyle tan(60^{\circ})=tan(\frac{\pi}{3})=\sqrt{3}\)
La fonction tangente n'est pas définie en \(\displaystyle \frac{\pi}{2}\) (\(\displaystyle 90^{\circ}\)).
\(\displaystyle tan(x + \pi)=tan(x)\)
Relations entre les fonctions trigonométriques
Principales relations entre les fonctions trigonométriques :
\(\displaystyle cos^2(x)+sin^2(x)=1\)
\(\displaystyle tan(x)=\frac{sin(x)}{cos(x)}\)
\(\displaystyle \frac{1}{cos^2(x)}=1+tan^2(x)\)
\(\displaystyle cotan(x)=\frac{1}{tan(x)}\)
\(\displaystyle cotan(x)=\frac{cos(x)}{sin(x)}\)
\(\displaystyle \frac{1}{sin^2(x)}=1+cotan^2(x)\)
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