sin(3x-П/6)=1/2, x[-2П;П]

Question

sin(3x-П/6)=1/2, x[-2П;П]

Answer 1

3x-П/6=П/6+2Пk

3x=П/3+2Пk

x=П/9+2Пk/3

П/9+2Пk/3<=П</p>

2/3k<=8/9  k<=(8/9)*(3/2)=4/3   k<=4/3  k=1  x=П/9+2П/3=7П/9</p>

 П/9+2Пk/3>=-2П

k>=-19/6

k=0 x=П/9

k=-1 x=-5П/9

k=-2 x=-11П/9

k=-3 x=-17П/9

 

3x-П/6=5П/6+2Пk

3x=П+2Пk

x=П/3+2Пk/3  k=0  x=П/3

                     k=1  x=П

                      k=-3  x=-5П/3

                      k=-2 x=-П

                       k=-1 x=-П/3