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Squared trigonometrics

  1. May 10, 2007 #1

    disregardthat

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    1. The problem statement, all variables and given/known data

    Hi, I wonder how to solve, and how to get the correct answer\answers to these types of problems:

    [tex]2 \sin^2{x} - 4 \cos^2{x} = 0[/tex] [tex] x \in [0°,360°] [/tex]

    There are many answers to this. I would really like to know how the correct way to get all of them.


    2. Relevant equations

    I do not know any relevant equations for this.


    3. The attempt at a solution

    I have tryed to divide them with [tex]\cos^2(x)[/tex] to get [tex] \tan^2(x)[/tex] But it has not worked.
     
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  3. May 10, 2007 #2

    cristo

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    Well, firstly can you reduce the expression to contain only one of sinx or cosx by using the relationship sin2x+cos2x=1?
     
  4. May 10, 2007 #3

    disregardthat

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    No, I do not know how to do it! :\
     
  5. May 10, 2007 #4

    HallsofIvy

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    Then you need to learn algebra! Since sin2x+ cos2x= 1, cos2x= 1- sin2x. Now replace cos2x in your equation by 1- sin2 x.
     
  6. May 10, 2007 #5

    disregardthat

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    Oh, I misunderstood. Of course...

    I found this equation:

    [tex]\cos^2(x) = \frac{1}{3}[/tex] But how do get all the answers? There are four.

    If i square root bot sides, I will get two answers, (which are correct) but not all of them... How is the right way?
     
  7. May 10, 2007 #6

    disregardthat

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    I just found out, I took the square root, and the answer must also be negative...
     
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