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Math Help - polar to parametric equation conversion.

  1. #1
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    polar to parametric equation conversion.

    Write the polar equation r = cos(4*theta) in the parametric form x = x(t), y = y(t)
    r = cos(4*theta), x = r * cos(theta), y = r * sin(theta)

    x = cos(4*t) * cos(t)

    y = cos(4*t) * sin(t)

    Do the functions have to be in terms of t or can they be in theta?


    Am I correct?
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  2. #2
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    I would take r = cos(4\theta) and multiply both sides by r

    this gives r^2= r\times cos(4\theta)

    and using r^2 = x^2+y^2

    r^2= r\times cos(4\theta) \Rightarrow x^2+y^2= x
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  3. #3
    Senior Member Spec's Avatar
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    That looks correct, and no, the variable doesn't really matter.
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  4. #4
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    Quote Originally Posted by pickslides View Post
    I would take r = cos(4\theta) and multiply both sides by r

    this gives r^2= r\times cos(4\theta)

    and using r^2 = x^2+y^2

    r^2= r\times cos(4\theta) \Rightarrow x^2+y^2= x
    r \cos (4 \theta) \neq x.

    Diroga's original solution was perfectly correct and adequate.

    As for the t, \theta business - if the question asks to have it in terms of t then put it in terms of t. This is just a matter of convention.
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