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Coordinate Systems

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Graph the surface in R3

    2. Relevant equations
    Spherical equation [tex]\rho[/tex] = 2asin([tex]\varphi[/tex])

    3. The attempt at a solution
    I think its just a sphere with a radius of 2
    _______________________________________________

    1. The problem statement, all variables and given/known data
    Graph the solid whose given coordinates satisfy the inequalities

    2. Relevant equations
    a) 0 [tex]\leq[/tex] r [tex]\leq[/tex] 3, 0 [tex]\leq[/tex] [tex]\theta[/tex] [tex]\leq[/tex] [tex]\pi[/tex]/2, -1 [tex]\leq[/tex] z [tex]\leq[/tex] 2
    b) 2r [tex]\leq[/tex] z [tex]\leq[/tex] 5 - 3r

    3. The attempt at a solution
    I figure these are cylinders because of variables used to describe the coordinates but besides that I'm having trouble know what to use the inequalities for
    _______________________________________________

    1. The problem statement, all variables and given/known data
    Graph the solid whose given coordinates satisfy the inequalities

    2. Relevant equations
    a) 0 [tex]\leq[/tex] [tex]\rho[/tex] [tex]\leq[/tex] 1, 0 [tex]\leq[/tex] [tex]\theta[/tex] [tex]\leq[/tex] [tex]\pi[/tex]/2,
    b) 0 [tex]\leq[/tex] [tex]\rho[/tex] [tex]\leq[/tex] 2/cos[tex]\varphi[/tex], 0 [tex]\leq[/tex] [tex]\varphi[/tex] [tex]\leq[/tex] [tex]\pi[/tex]/4

    3. The attempt at a solution
    Spheres, but same problem as with the others, I'm just not doing well at understanding how to use the inequalities to graph it
     
  2. jcsd
  3. Oct 16, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi STLCards002! :smile:

    Sorry, but everything is wrong. :cry:

    The only thing I can suggest is that you draw a nice big diagram (take up a whole page), with x y and z axes marked, and just draw in the boundaries.

    If it helps, pretend the inequalities are equalities … that will give you the boundaries, and you can work out which parts to shade, later.
     
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