Équations Trigonométriques - Terminale
Terminale
Équations Trigonométriques
Équations de base
cos(x) = a
x = ±arccos(a) + 2kπ
sin(x) = b
x = arcsin(b) + 2kπ ou π - arcsin(b) + 2kπ
Valeurs remarquables
cos(0) = 1, cos(π/2) = 0, cos(π) = -1
sin(0) = 0, sin(π/2) = 1, sin(π) = 0
cos(π/3) = 1/2, sin(π/6) = 1/2
Exemple
2cos²(x) - cos(x) - 1 = 0
On pose X = cos(x) : 2X² - X - 1 = 0
X = 1 ou X = -1/2
x = 0 [2π] ou x = ±2π/3 [2π]