1. Not finding help here? Sign up for a free 30min 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!

Sketching the Image of a Multivariable Function

  1. Jul 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Let f:R^2 to R^2 be defined by f(r,theta) = (rcos(theta), rsin(theta))

    Sketch the image under f of the set S = (1,2) X (0,pi) (The open brackets should be closed brackets but Im on a foreign keyboard and cant figure out how to get closed brackets).


    2. Relevant equations
    Unsure


    3. The attempt at a solution
    I am unsure how to sketch something going from R^n to R^m in general, so I have no attempt at a solution. Any hints would be greatly appreciated.
     
  2. jcsd
  3. Jul 9, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The equation S = (1,2) X (0,pi) defines a region S in R2. What you need to do is draw a 2D picture of the region in R2 that S is mapped to under the function f. Presumably you know whether S is described with (x,y) coordinates or ##(r,\theta)## coordinates.
     
  4. Jul 9, 2012 #3
    Oic, so essentially I'm going to be drawing a circle with an inner radius of 1 and an outer radius of 2? If so, this question was much easier than I thought. Thanks a lot for your help.
     
  5. Jul 9, 2012 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If the coordinates for S are polar coordinates, what you are describing is the shape of S, which is the domain, except the upper variable is ##\pi##, not ##2\pi##. You wouldn't get the whole circles. If I understand the problem correctly, you need a picture of what it is mapped to.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sketching the Image of a Multivariable Function
  1. Multivariable sketch (Replies: 4)

  2. Multivariable Function (Replies: 1)

  3. Sketching Functions (Replies: 1)

Loading...