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Homework Help: 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



  4. Jan 21, 2015 #3


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    Homework Helper

    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
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