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Math Help - find intersetion points

  1. #1
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    find intersetion points

    how do you find the points of intersection algebraicly?
    1-cos(theta) = 1+cos(theta)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jeph View Post
    how do you find the points of intersection algebraicly?
    1-cos(theta) = 1+cos(theta)
    let theta be x

    1 - cos(x) = 1 + cos(x)
    => 1 = 1 + 2cos(x) ............added cos(x) to both sides
    => 0 = 2cos(x) .................subtracted 1 form both sides.

    so we want all x's such that

    2cos(x) = 0
    => cos(x) = 0
    => x = cos^-1(0)
    => x = pi/2 + k*pi
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  3. #3
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    dont the curves intersect at 0 also? do i need to plug in the pi/2 into just 1 of the equations to find the intersection?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jeph View Post
    dont the curves intersect at 0 also? do i need to plug in the pi/2 into just 1 of the equations to find the intersection?
    the curves DO NOT intersect at 0

    remember cos(0) is 1

    so 1 - cos(0) = 1 - 1 = 0

    and 1 + cos(0) = 1 + 1 = 2

    so 1 - cos(x) is not equal to 1 + cos(x) at x = 0

    no, pluging in is not necessary, the intersection points are the values of x (which is what i called theta) i gave you.

    below is a graph that show some of the intersections

    the graph intersects for pi/2 and every multiple of pi before and after that
    Attached Thumbnails Attached Thumbnails find intersetion points-cos.gif  
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  5. #5
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    Hello, jeph!

    Find the points of intersection: .1 + cosθ .= .1 - cosθ
    I assume these are polar curves (two cardioids).
    . . Jhevon was absolutely correct.

    We have: .2·cosθ = 0 . . cosθ = 0 . . θ = ±½π


    The points of intersection are: .(1, ½π), (1, -½π)

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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, jeph!

    I assume these are polar curves (two cardioids).
    . . Jhevon was absolutely correct.

    We have: .2·cosθ = 0 . . cosθ = 0 . . θ = ±½π


    The points of intersection are: .(1, ½π), (1, -½π)

    is there any particular reason you assumed they were polar curves, Soroban?
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  7. #7
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    Hello, Jhevon!

    is there any particular reason you assumed they were polar curves, Soroban?

    Well, just their appearance, especially the use of θ (theta).

    It suggested an "Area between two polar curves" problem . . .
    In this case: .r .= .1 + cosθ .and .r .= .1 - cosθ
    . . and theor intersections (polar coordinates) must be determined.

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