Найдите корни уравнения sin(4x/5+2п/3)=-1/2

Question

Найдите корни уравнения sin(4x/5+2п/3)=-1/2

Answer 1

4x/5+2π/3=-π/6+2πn,n∈z U 4x/5+2π/3=7π/6+2πk,k∈z
4x/5=-5π/6+2πn,n∈z U 4x/5=π/2+2πk,k∈z
x=-25π/24+5πn/2,n∈z U x=5π/8+5πk/2,k∈z