ReoCLIK - Définition de base des fonctions trigonométriques - Les fonctions trigonométriques - Mathématiques

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04/05/2025

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• Mathématiques > Les fonctions trigonométriques > Définition de base des fonctions trigonométriques

Définition de base des fonctions trigonométriques

La fonction cosinus

Valeurs particulières de la fonction cosinus (cos) :

c o s (0^{\circ}) = c o s (0) = 1

c o s (30^{\circ}) = c o s (\frac{π}{6}) = \frac{\sqrt{3}}{2}

c o s (45^{\circ}) = c o s (\frac{π}{4}) = \frac{\sqrt{2}}{2}

c o s (60^{\circ}) = c o s (\frac{π}{3}) = \frac{1}{2}

c o s (90^{\circ}) = c o s (\frac{π}{2}) = 0

c o s (x + 2 π) = c o s (x)

La fonction sinus

Valeurs particulières de la fonction sinus (sin) :

s i n (0^{\circ}) = s i n (0) = 0

s i n (30^{\circ}) = s i n (\frac{π}{6}) = \frac{1}{2}

s i n (45^{\circ}) = s i n (\frac{π}{4}) = \frac{\sqrt{2}}{2}

s i n (60^{\circ}) = s i n (\frac{π}{3}) = \frac{\sqrt{3}}{2}

s i n (90^{\circ}) = s i n (\frac{π}{2}) = 1

s i n (x + 2 π) = s i n (x)

La fonction tangente

Valeurs particulières de la fonction tangente (tan) :

t a n (0^{\circ}) = t a n (0) = 0

t a n (30^{\circ}) = t a n (\frac{π}{6}) = \frac{\sqrt{3}}{3}

t a n (45^{\circ}) = t a n (\frac{π}{4}) = 1

t a n (60^{\circ}) = t a n (\frac{π}{3}) = \sqrt{3}

\frac{π}{2}

90^{\circ}

t a n (x + π) = t a n (x)

Relations entre les fonctions trigonométriques

Principales relations entre les fonctions trigonométriques :

c o s^{2} (x) + s i n^{2} (x) = 1

t a n (x) = \frac{s i n (x)}{c o s (x)}

\frac{1}{c o s^{2} (x)} = 1 + t a n^{2} (x)

c o t a n (x) = \frac{1}{t a n (x)}

c o t a n (x) = \frac{c o s (x)}{s i n (x)}

\frac{1}{s i n^{2} (x)} = 1 + c o t a n^{2} (x)

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