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!

Converting parametric to cartesian

  1. Jan 21, 2015 #1
    (This is actually a calculus problem, not a physics one, but physics is based on calculus, so I hope it's fine)

    1. The problem statement, all variables and given/known data

    Eliminate the parameter to find the Cartesian equation of x = (1/2)cos(θ) y = 2sin(θ)

    2. Relevant equations
    x^2 + y^2 = 1 (eq of circle)

    3. The attempt at a solution
    First approach: x^2 + y^2 = (1/4)cos^2(θ) + 4sin^2(θ) = ?
    I can't get rid of θ because the constant preceding cosine and sine are not equal.

    2nd try: y/x = 2sin(θ)/(0.5cos(θ)) = 4 * (sin(θ)/cos(θ)) = y/4x = tan(θ), so θ = arctan(y/4x)
    But θ is still there. I need an answer in x and y.

    Thank you for your help.
     
  2. jcsd
  3. Jan 21, 2015 #2
    It is useful to note that

    ##sin(arctan(x))~=~\frac{x}{\sqrt{1+x^2}}##

    and

    ##cos(arctan(x))~=~\frac{1}{\sqrt{1+x^2}}##
     
  4. Jan 21, 2015 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Do not assume it is a circle. It is not.

    Arrange the equations so as cosθ and sinθ are alone on one side of the equations: cosθ= ? sinθ = ?
    Take the square of both equations and add them together.
     
  5. Jan 21, 2015 #4
    Thank you
     
  6. Jan 21, 2015 #5
    Following your method, I got 4x^2 + (y^2)/4 = 1
    My textbook doesn't have an answer key, but I am going to assume that this is the correct answer. Thank you very much
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Converting parametric to cartesian
  1. Cartesian vectors (Replies: 3)

  2. Cartesian Coordinates (Replies: 5)

Loading...