Question

Salutare !
cos(x)=-1/2
Ma intereseaza metoda de rezolvare,nu rezultatul final :D

Answer 1

cos x =-1/2 ⇔ x= +/- arccos (-1/2) + 2kπ , k∈Z
arccos(-1/2)=π- arccos(1/2)= π-π/3= 2π/3
1) x= 2π/3 + 2kπ
k=0⇒ x=2π/3 ∈ [0,π]
k=1⇒ x=2π/3+2π ∉ [0,π]
2) x= -2π/3 + 2kπ
k=0⇒ x=-2π/3 ∉ [0,π]
k=1⇒ x= -2π/3+ 2π= 4π/3 ∉ [0,π]
⇒ S= {2π/3}