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Convert space curve to cartesian

  1. Feb 14, 2004 #1
    if R = sinti+sqrt(2)costj+sintk, 0<=t<=Pi/2
    please eliminate t to determine the cartesian equation of R(t). Put limits on the variables and verbally describe the curve
  2. jcsd
  3. Feb 15, 2004 #2
    x= sint, y=sqrt(2)cost, z=sint

    u can clearly see that
    x2 + y2 +z2=2{sin2t +cos2t}


    x2 + y2 +z2=2
  4. Feb 15, 2004 #3

    matt grime

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    And eqaully clearly, surely you can see there is more to it than that? You've just replaced a locally 1-d structure (a curve) with a locally 2-d structure, a sphere.

    yes, the x, y, and z coordinates necessarily satisfy that, but that isn't sufficient. You need to intersect with the plane x=z (or similar) at the very least.

    generally the equation is [tex]x=z=(1-y^2)^{1/2}/\sqrt 2[/tex]
  5. Feb 15, 2004 #4
    Thanks matt grime, i've checked yours is correct.
    but can you show me how the above equation is reached.
  6. Feb 15, 2004 #5


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    If matt grime will forgive me for sticking in my oar:

    x= sint, y=sqrt(2)cost, z=sint so obviously x= z.

    x2= sin2t= (1-cos2t). But
    y2= 2 cos2t so cos2t= y2/2. That is x2= 1- y2/2 and
    x= z= &radic;(1- y2/2).
    Last edited by a moderator: Feb 17, 2004
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