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Please help with trig equation!

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data
    cosθ = sin2θ/2


    2. Relevant equations
    None.


    3. The attempt at a solution
    I really don't know what to do. I tried using the half and double angle identities and this is what I got:
    cosθ = (1-cos2θ)/2
    2cosθ = 1-cos2θ
    2cosθ + cos2θ = 1
    2cosθ + 2cos2θ -1 = 1
    2(cosθ + cos2θ) = 2
    cosθ + cos2θ = 1
    cos2θ + cosθ - 1 = 0

    I'm not sure if that can be factored, so I tried using the quadratic formula. I got (-1 ± √5)/2
    What am I supposed to do now? I don't even know if I did this right. Someone pleeeaase help mee ):
     
    Last edited: Apr 4, 2012
  2. jcsd
  3. Apr 5, 2012 #2
    Your very first step is wrong: [itex]sin^2(\theta) \neq 1-cos(2\theta)[/itex]

    I would suggest writing [itex]sin^2(\theta)[/itex] in terms of [itex]cos^2(\theta)[/itex] right from the start! You'll end up with a quadratic equation, similar in form as your last equation you gave (which is wrong!). When you solve this quadratic equation, what exactly is set equal to the answer?
     
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