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Vector equation

  1. Jan 16, 2017 #1
    1. The problem statement, all variables and given/known data
    Suppose that a particle follows the path
    r(t) = 2cos(t)i + 2sin(t)j
    Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle.

    2. Relevant equations
    None that come to mind

    3. The attempt at a solution
    I set x = 2cos(t) and y = 2sin(t)
    thus t = arcsin(y/2)
    then x = 2cos(arcsin(y/2))
    then x - 2cos(arcsin(y/2)) = 0

    It says that this is wrong
    I am not all to familiar with doing this type of problem though I suspect that the inverse trigonometric could be messing up the domain of the solution

    This is the last problem I need for the homework so any help would be much appreciated
     
  2. jcsd
  3. Jan 16, 2017 #2

    LCKurtz

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    Try squaring ##x## and ##y## and see if anything comes to mind.
     
  4. Jan 16, 2017 #3

    BvU

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    Can you draw a few points of the path ? Take easy values for ##t##, like ##{\pi\over 6},\ {\pi \over 4},\ {\pi\over 3}\ ## etc.
     
  5. Jan 16, 2017 #4
    Alright I finally got it
    r(t) = 2cos(t)i + 2sin(t)j
    x = 2cos(t)
    y = 2sin(t)
    x^2 = 4cos^2(t)
    y^2 = 4sin^2(t)
    x^2+y^2=4
    x^2+y^2-4=0
    This answer was accepted as correct
    I did not even think about squaring the variables thanks
     
  6. Jan 16, 2017 #5

    Ray Vickson

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    Whenever you see ##\sin(at)## and ##\cos(at)## appearing together in some equation or parametrization, you should always look at what happens when you square them. Sometimes squaring will not work, but sometimes it solve a problem very easily---all you can do is try it and see.
     
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