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marasofia1616

Find all solutions to the equation in the interval [0, 2π). cos 2x - cos x = 0

  • one year ago
  • one year ago

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  1. hieuvo
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    so, cos2x=cosx, I think x is in those special angles

    • one year ago
  2. RadEn
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    use identity : cos2x=2cos^2 x - 1

    • one year ago
  3. RadEn
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    so, we have a quadratic equation in form cosx, 2cos^2 x - 1 - cosx = 0 or 2cos^2 x - cosx - 1 = 0 can u factor out it

    • one year ago
  4. marasofia1616
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    ok I get cos x(2 cos x-1)=1

    • one year ago
  5. RadEn
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    np, it should be (2cosx + 1)(cosx - 1) = 0

    • one year ago
  6. RadEn
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    now, for zeroes take each factors be zero, so 2cosx+1=0 or cosx-1=0 solve for x

    • one year ago
  7. marasofia1616
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    ok I got the solutions 0, 2pi/3 and 4pi/3

    • one year ago
  8. marasofia1616
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    thank you

    • one year ago
  9. RadEn
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    but, i miss one root :)

    • one year ago
  10. RadEn
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    looks 0 be same for 2pi, right ?

    • one year ago
  11. marasofia1616
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    I got the answer right

    • one year ago
  12. RadEn
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    ok, great..

    • one year ago
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