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Understanding Spherical Coordinates

  1. Dec 5, 2012 #1
    questioning what ρ does. What is the difference between the two equations?

    Let k be the angle from the positive z-axis and w be the angle from the pos x-axis

    parametric equation of a sphere with radius a
    paramet eq. 1:
    x = asin(k)cos(w)
    y = asin(k)sin(w)
    z= acos(k)

    0≤w≤2pi
    0≤k≤pi
    a is constant

    paramet equ 2:
    x = ρsin(k)cos(w)
    y = ρsin(k)sin(w)
    z= ρcos(k)
    0≤w≤2pi
    0≤k≤pi
    0≤ρ≤a

    Is the first equation the surface of the sphere and the second would be the equation of a solid sphere?

    second question: Look in paint document:
    I originally thought that ρ = constant (which is the distance from the origin to the point) was the entire line segment from the origin to the point. But if my understanding is correct the coordinate ρ actually represents some point ρ units aways from the origin. Is this correct?
     

    Attached Files:

  2. jcsd
  3. Dec 5, 2012 #2

    pasmith

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    Homework Helper

    Yes.

    Yes.
     
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