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Parametric Representation in Spherical and Cartesian coordinates

  1. Oct 4, 2011 #1
    Give a parametric representation of the following surfaces in terms of the given parameter variables:
    a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi.
    b)The graph of the function z = (x^3) - sqrt(y) in terms of the Cartesian variables x and y.

    I'm not sure how to do these at all.
    a) It's a sphere and theta ranges from 0 to pi/2. phi ranges from 0 to pi/2. Are the parametric equations just theta = t and phi = t, given that t ranges from 0 to pi/2? Or do we substitute x = psin(phi)cos(theta), etc. I'm really not sure what to do. Help.
     
  2. jcsd
  3. Oct 4, 2011 #2

    vela

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    The surface is two-dimensional, so you need two parameters to describe it. The problem told you to use θ and Φ as your parameters. These parameters independently vary from 0 to π/2. Now you want to come up with some equation of the form r = f(θ,Φ).
     
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