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Math Help - Finding the intersection point of these:

  1. #1
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    Finding the intersection point of these:

    Find the intersection point of:

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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Find the intersection point of:

    Call theta = t for convenience.

    The second equation says:
    cos(t) = 1/r (For r not equal to 0)

    So the first equation says:
    r(1/r - pi/4) = sqrt(2)

    Now you solve it from here.

    -Dan
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  3. #3
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Find the intersection point of:

    Are you sure that the first equation is not:

    r cos(theta -pi/4) =sqrt(2)

    RonL
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  4. #4
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    Ohhhhh sorry for that ....

    Here itis
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Ohhhhh sorry for that ....

    Here itis
    See here.

    -Dan
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  6. #6
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    Hello, ^_^Engineer_Adam^_^!

    Find the intersection point of: .r·cos(θ - ¼π) .= .√2 .and .r·cosθ .= .1

    The first curve is: .r·(cosθ·cos¼π + sinθ·sin¼π) .= .√2

    . . r·(cosθ·½√2 + sinθ·½√2) .= .√2 . . r·(cosθ + sinθ) .= .2

    . . Then: .r·cosθ + r·sinθ .= .2 . . x + y .= .2


    The second curve is: .r·cosθ .= .1 . . x = 1


    The intersection of the two lines is: .(1, 1)

    . . In polar coordinates: .(√2, ¼π)

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    If they insist on a general solution:

    . . (√2, π/4 + 2kπ) .and .(-√2, 5π/4 + 2kπ) .for any integer k.



    Edit: Thanks for the heads-up, Dan. .I fixed my blunder.
    Last edited by Soroban; March 17th 2007 at 07:47 AM.
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Soroban View Post
    If they insist on a general solution:

    . . (√2, π/4 + 2kπ) .and .(-√2, 3π/4 + 2kπ) .for any integer k.

    Ummm...
    tan(3*pi/4) = -1, not 1! I think you were thinking of 5*pi/4?

    -Dan
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