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Parametric Equations - Finding Tangent Lines

  1. Jul 29, 2009 #1
    So I'm looking at this example in my textbook where they're trying to find the vert. & horizontal tangent lines of r = sin Θ, 0 < Θ < pi. they say to first change it to parametric equations where

    x = r cos Θ = sin Θ cos Θ
    and
    y = r sin Θ = sin Θ sin Θ = sin^2 Θ

    But now I'm just really confused, how did they get these parametric equations?
     
  2. jcsd
  3. Jul 29, 2009 #2
    It's a simple conversion from polar to cartesian coordinates.

    The definition of the conversion (I'm sure this is in your textbook) is:

    x = r * cos Θ
    y = r * sin Θ

    However, you're given r as a function of Θ - i.e., r(Θ).

    So the conversion becomes:

    x = r(Θ) * cos Θ
    y = r(Θ) * sin Θ

    Simply replace r(Θ) with its definition (i.e., r(Θ) = sin Θ)

    x = sin Θ * sin Θ
    y = sin Θ * cos Θ
     
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