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I have been given this equation: $$\rho = \cot (\phi)$$

I have been asked to "describe it in spherical coordinates", giving a verbal explanation.

My work: I assume that the equation is given in standard cylindrical coordinates, $\rho,\phi,z$. So the projection onto the $x-y$ or $z=0$ plane looks like this:

enter image description here

However, I am not sure how to translate it into cylindrical coordinates, or what is meant by a verbal explanation.

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    $\begingroup$ Could you explain a little more. Presumably $\rho,\phi,z$ are cylindrical coordinates. So your equation is effectively the equation of a curve in the $x,y$ plane. Presumably the corresponding surface allows any value of $z$, so you translate the curve parallel to the $z$-axis. Is that how you interpret the question? If not, what do you think it means? $\endgroup$ – almagest Jul 1 '16 at 17:42
  • $\begingroup$ It's in spherical coordinates (p, theta, phi). And yes that is the way I interpret the question. $\endgroup$ – Math Jul 2 '16 at 21:01
  • $\begingroup$ @AlanTarn You ran into a key feature of this site. Most of the answers are provided by academics, or students who want to become academics. They do not like what they see as laziness. So they are unenthusiastic about what look like homework questions, particularly when it appears that the OP (jargon for the person who asked the question) has not made any effort himself (or herself). I am about to edit the question slightly in the hope that it might be reopened. You then need to add a paragraph about what you have tried and why you are stuck. $\endgroup$ – almagest Jul 3 '16 at 7:38
  • $\begingroup$ @AlanTarn. Please edit my edits. I am guessing somewhat at where your difficulty lies and where you are quoting from what you have been given and where you were asking MSE a question. $\endgroup$ – almagest Jul 3 '16 at 7:46

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