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: Parametrizing a curve

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Find a vector-valued function f that parametrizes the curve (x-1)^2 + y^2 = 1

    2. Relevant equations

    (x-1)^2 + y^2 = 1

    3. The attempt at a solution

    The equation is the graph of a circle that is 1 unit to the right of the origin, therefore a parametrization would be

    x(t) = cos(t) + 1
    y(t) = sin(t)

    Therefore a vector-valued function that parametrizes this curve is given by

    r(t) = (cos(t) + 1)i + sin(t)j

    I've been having trouble with parametrization lately so I was wondering if this is correct. Also, is there a better method to go about this sort of thing? Is it entirely visual and you just have to have a "feel" for it?
  2. jcsd
  3. Jan 16, 2013 #2


    User Avatar
    Gold Member

    Yes, that would be a correct parametrisation. There are of course ways to check that it is correct.
  4. Jan 16, 2013 #3
    But is there an algorithm or anything to go about it? I just had to visualize it. Will every parametrization problem be like that?
  5. Jan 16, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I would say pretty much yes to that. There are always many possible parameterizations and often some are more natural or "better" than others for a particular purpose. In your example, visualizing it as a circle and thinking in terms of sines and cosines is exactly the appropriate approach. There isn't a magic procedure that will always mindlessly work.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook