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marasofia1616

  • 3 years ago

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

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

  2. RadEn
    • 3 years ago
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    use identity : cos2x=2cos^2 x - 1

  3. RadEn
    • 3 years ago
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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

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

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

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

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

  8. marasofia1616
    • 3 years ago
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    thank you

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

  10. RadEn
    • 3 years ago
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    looks 0 be same for 2pi, right ?

  11. marasofia1616
    • 3 years ago
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    I got the answer right

  12. RadEn
    • 3 years ago
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    ok, great..

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