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Math Help - Find vector function

  1. #1
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    Find vector function

    First off i have a problem that the teacher somewhat worked out on the board.
    I am not sure how he got the answer.

    Find the vector function that represents the curve of intersection of the two surfaces.

    The cylinder.
    x^2 + y^2 = 4

    and the surface z=xy

    Attempt:

    r=2

    x= 2cost
    y=2sint
    z=(2cost)(2sint)

    Now, from here i think the teacher used the product rule? I am not sure.

    Solving for z

    z=2sin2t

    I tried the product rule but couldnt get it. Could someone work out the steps on how he got the answer?

    Thank you
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  2. #2
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    Re: Find vector function

    Not the product rule - your teacher used the trigonometric identity \sin{2t}=2\sin{t}\cos{t}.

    - Hollywood
    Thanks from icelated
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  3. #3
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    Re: Find vector function

    Quote Originally Posted by hollywood View Post
    Not the product rule - your teacher used the trigonometric identity \sin{2t}=2\sin{t}\cos{t}.

    - Hollywood
    That he did. Thank you!
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