Question

Тема: Тригонометрические уравнения

Answer 1

1) 2*sin(x-π/6)=-1  |÷2

sin(x-π/6)=-1/2

x-π/6=7π/6+2πn        x₁=8π/6+2πn=4π/3+2πn

x-π/6=-π/6+2πn         x₂=2πn.

2) 2*sin(4x)+√3=0

2*sin(4x)=-√3  |÷2

sin(4x)=-√3/2

4x=4π/3+2πn   |÷4       x₁=π/3+πn/2.

4x=5π/3+2πn  |÷4        x₂=5π/12+πn/2.

3) 2*cos(3x)+√3=0

2*cos(3x)=-√3  |÷2

cos(3x)=-√3/2

3x=5π/6+2πn   |÷3       x₁=5π/18+2πn/3

3x=7π/3+2nn   |÷3         x₂=7x/18+2πn/3.