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: Cartesian equation

  1. Dec 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Give a Cartesian equation for the parametric curve x(t)=3sin(2t) and y=4cos(2t)

    2. Relevant equations

    3. The attempt at a solution
    I'm not sure if i'm doing this right
    since x^2+y^2=1

    I thought

    sin^2(2t)+cos^2(2t)=1 should be the right answer
    am i wrong
    so how do you go about converting parametric curve to a cartesian equation
    Last edited: Dec 11, 2007
  2. jcsd
  3. Dec 11, 2007 #2


    User Avatar
    Science Advisor

    You want an equation that involves x and y only, and not t.

    And I can't tell if sin2(t) is supposed to mean sin^2(t) or sin(2t). Either way, can you express cos(2t) in terms of sin2(t)? Once you do that, you're basically done.
  4. Dec 11, 2007 #3
    If you have taken a calculus III course at all (looks like you are taking one right now)the questions are reversed and stated as parameterize the following. If you think in a reverse way, you may get some insight.

    Look up ellipse in the form of ...oops I'm not supposed to give out the answer!
  5. Dec 11, 2007 #4


    User Avatar
    Science Advisor

    Do you mean x= 3sin(2t)?

    Where did you get that?

    No, sin^2(2t)+cos^2(2t)=1 is a good start but it is not the "answer"!

    Assuming you meant x= 3 sin(2t) then x/3= sin(2t). If y= 4 sin(2t) then y/4= sin(2t). Now, what do you get if you square both sides of those equations and then add?
  6. Dec 11, 2007 #5
    sorry i meant 3sin(2t)

    okay so if you are supposed to square both side of the equation you should get
    how did you get y=4sint(2t)?
    but if you were to square that you would get y^2/16=sin^2(2t)
    then if you add the two equations
    is that what you mean?
  7. Dec 11, 2007 #6


    User Avatar
    Gold Member

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook