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If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data

    If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

    2. Relevant equations

    3. The attempt at a solution
    θ is in quadrant 2 or 3

    in quadrant 2:
    related acute = cos[itex]^{-1}[/itex](5/13)
    = 1.18
    θ = π - 1.18
    = 1.96 radians

    in quadrant 3:
    related acute angle = 1.18
    θ = π + 1.18
    = 4.32 radians

    Those are the two values I got for θ. But my book says the answer is 5.14. Can you tell me where I am going wrong?
  2. jcsd
  3. Nov 4, 2013 #2


    User Avatar
    Homework Helper

    Where didn't you go wrong???

    Nah, I'm just kidding :biggrin: The book's answer is wrong, you're right. They accidentally included the angle in the 4th quadrant rather than the 3rd as you've correctly done.
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