Найдите корни уравнения ** заданном промежутке Sin 3x= √2\2, [0;2Π]

Question

Найдите корни уравнения на заданном промежутке
Sin 3x= √2\2, [0;2Π]

Answer 1

3x=π/4+2πn U 3x=3π/4+2πk
x=π/12+2πn/3 U x=π/4+2πk/3
0≤π/12+2πn/3≤2π
0≤1+8n≤24
-1≤8n≤23
-1/8≤n≤23/8
n=0⇒x=π/12
n=1⇒x=π/12+2π/3=9π/12=3π/4
n=2⇒x=π/12+4π/3=17π/12
0≤π/4+2πk/3≤2π
0≤3+8k≤24
-3≤8k≤21
-3/8≤k≤21/8
k=0⇒x=π/4
k=1⇒x=π/4+2π/3=11π/12
n=2⇒x=π/4+4π/3=19π/12