SOLUTION: Solve this equation for {{{"[0,"}}}{{{2pi}}}{{{")"}}}: {{{Sin(4x) - Sin(2x)=0}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Solve this equation for {{{"[0,"}}}{{{2pi}}}{{{")"}}}: {{{Sin(4x) - Sin(2x)=0}}}      Log On


   

Question 335877: Solve this equation for %22%5B0%2C%222pi%22%29%22:
Sin%284x%29+-+Sin%282x%29=0
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
Solve this equation for %22%5B0%2C%222pi%22%29%22:
Sin%284x%29+-+Sin%282x%29=0

Write 4 in the first term as 2%2A2  

Sin%282%2A2x%29+-+Sin%282x%29=0

Use the identity Sin%282theta%29=2%2ASin%28theta%29%2ACos%28theta%29 with theta=2x
to replace the first term:

2%2ASin%282x%29%2ACos%282x%29+-+Sin%282x%29=0

Factor out Sin%282x%29 on the left:

Sin%282x%29%282Cos%282x%29-1%29=0

Set each factor on the left = 0



Notice that the coefficient of x is 2.
Since we want all values x in the interval
%22%5B0%2C%222pi%22%29%22, we must find all values for 
2x in the interval %22%5B0%2C%224pi%22%29%22



So there are 8 solutions. 
  
Edwin