Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook