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CAL 3 concept

  1. Sep 26, 2005 #1
    i have the parametric equations to the curve X = cos t y = sin t and z = t

    which of the following surfaces does it lie on?

    1)circular cylinder
    2)elliptic paraboloid

    I think theres more than one answer but i cant seem to picture it from the equation on why. Anyone know y?
  2. jcsd
  3. Sep 26, 2005 #2
    The x-y traces are circles. X^2+y^2 = cos(t)^2 + sin(t)^2 =1
    Z=t, which means the height increases with the variable t.

    Its going to lie on a circular cylinder, but it will be in the shape of a HELIX, wrapped around that cylinder of course.
  4. Sep 26, 2005 #3
    Hey thanks for the answer but how could u just take an x^2 + y^2 = cos(t)^2 + sin(t)^2 = 1 just like that??

    im lookin athe parametrics and i see no sqs... how could u know its sqs and not like x^3 or something??
  5. Sep 26, 2005 #4
    practice. You will easily recognize tricks like that too with time. X^3 would do you no good, because its not a trig identity; however, the x,y^2s do allow u to use a trig identity.
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