Question

Find all solutions to the equation in the interval [0, 2π). (3 points) sin 2x - sin 4x = 0

pi divided by six , pi divided by two , five pi divided by six , seven pi divided by six , three pi divided by two , eleven pi divided by six

0, pi divided by six , pi divided by two , five pi divided by six , π, seven pi divided by six , three pi divided by two , eleven pi divided by six

0, two pi divided by three , four pi divided by three

0, pi divided by three. , two pi divided by three. , π, four pi divided by three. , five pi divided by three.

Answer 1

Explanation:

Answer:

Explanation:

hello :

in the interval [0, 2π). sin 2x - sin 4x = 0 means :

sin 2x =sin 4x

all solutions in R :4x=2x+2kπ or 4x = π -2x +2k'π k , k' in Z

2x = 2kπ or 6x= (2k'+1)π

x = kπ or x = (2k'+1)π/6

in : [0, 2π) k =0 k =1 so : x=0 x=π

k' = 0 , k' =1 , k' = 2 , k'=3 , k'= 4 , k' = 5

so x= π/6 x= π/2 x= 7π/6 x= 3π/2 x= 11π/6