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Trigonometric Equations

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data
    sin 2θ = sin θ Find the solutions in degrees.


    2. Relevant equations

    sin 2θ = 2sinθcosθ

    3. The attempt at a solution
    sin 2θ = sin θ
    2sinθcosθ = sin θ
    sinθ *cosθ/sin θ = 1

    That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ?
     
  2. jcsd
  3. Feb 23, 2009 #2

    HallsofIvy

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    Science Advisor

    One obvious possibility is [itex]sin(\theta)= 0[/itex]. What values of [itex]\theta[/itex] give that?
    IF [itex]sin(\theta)\ne 0[/itex], you can divide by it.

    So cancel the [itex]sin(\theta)[/itex]s, giving [itex]cos(\theta)= 1[/math]. What values of [itex]\theta[/itex] give that?

     
  4. Feb 23, 2009 #3
    Therefore the answer would be 0 degrees and 180 degrees? The book states that answers must greater or equal to one and less than 360.
     
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