1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Half-plane in R^3

  1. Sep 28, 2014 #1
    1. The problem statement, all variables and given/known data

    Describe in words the surface whose equation is given by theta = pi/4

    2. The attempt at a solution

    It is a fairly simple question, but I'm just trying to understand why this is considered a half-plane that exists for x that is greater than or equal to 0. There are no restriction on r or z. Given this, cannot r be negative? Wouldn't this make a full-plane and let it extend for x less than 0? I just don't quite see why it cannot have the point (-1, pi/4, 0), for example, which would be present for x less than 0. Any feedback is always appreciated!
  2. jcsd
  3. Sep 28, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    First of all, you haven't told us what coordinate system you are using. ##\theta = \frac \pi 4## makes sense in 2D polar coordinates, 3D cylindrical coordinates, and in spherical coordinates. In spherical coordinates it might be a plane or cone, depending on what convention you use for ##\theta##.

    But, to answer your question, you seem to understand what is going on perfectly well. Texts are inconsistent about whether or not ##r<0## is used in polar or cylindrical coordinates. If you are using the convention ##r\ge 0## you get a half plane as you say, and if ##r## is allowed to go negative you get the whole plane, as you understand. One problem with disallowing negative values of ##r## is that you don't see all 3 leaves of the rose ##r = \sin(3\theta)## for ##0\le\theta\le \pi##.

    I wouldn't worry too much about this if I were you since you understand it just fine.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted