Bonjour,
1) M est l'image de a et N l'image de b tels que a et b ∈ [0;π]
cos(a) = √3/2 ⇒ a = π/6
cos(b) = -1/2 ⇒ b = 2π/3
⇒ Arc(MN) = b - a = 2π/3 - π/6 = 4π/6 - π/6 = 3π/6 = π/2
2) a)
sin(a) = √2/2 et cos(a) > 0 ⇒ a = π/4
sin(b) = -1/2 et cos(b) < 0 ⇒ b = 7π/6
Arc(MN) = b - a = 7π/6 - π/4 = 14π/12 - 3π/12 = 11π/12
b)
sin(a) = 1 et cos(a) = 0 ⇒ a = π/2
cos(b) = √3/2 et sin(b) < 0 ⇒ b = 11π/6
Arc(MN) = b - a = 11π/6 - π/2 = 11π/6 - 3π/6 = 8π/6 = 4π/3
