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Homework Help: Express the equation in rectangular coordinates

  1. Oct 5, 2012 #1
    1. The problem statement, all variables and given/known data
    An equation is given in spherical coordinates. Express the equation in rectangular coordinates.


    So first thing I did was used a half angle formula

    r2 (cos2∅-sin2∅=z

    Now, i'm stuck.

    The answer is x2-y2=z

    Guidance is appreciated (:

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 5, 2012 #2


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    That looks fine.

    (You might like to use a symbol such as theta, θ, for an angle rather than the symbol used for the null set, ∅ . I don't know why phi, ϕ, is not include in the symbol box.)
  4. Oct 5, 2012 #3
    Thanks for the response and sorry for the minor errors, I'm still a bit confused on how I can manipulate what I have to make it to look more like x^2-y^2=z.

    What i'm thinking is if I just distribute the r^2. I will get (r^2cosθ^2)-(r^2sinθ^2)=z

    and if rcosθ=x and rsinθ =y

    then these are just the same values but squared. Which would give me X^2-y^2=z.

    Would that be a correct assumption?
  5. Oct 5, 2012 #4


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    I assume that ∅ is meant to be [itex]\phi[/itex]?

    There are 2 common conventions for spherical coordinates [itex](r, \theta, \phi)[/itex]. In one convetion,[itex]\theta[/itex] is the polar angle and [itex]\phi[/itex] is the azimuthal angle[/itex], and vice versa in the other convention. Which convention are you using?

    What are [itex]x[/itex], [itex]y[/itex], and [itex]z[/itex] in terms of spherical coordinates? What is [itex]x^2-y^2[/itex]?
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