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Understanding Parametric Equations and Curves Through Real-Life Examples

This lesson explores parametric equations, defined by functions (x = f(t)) and (y = g(t)), where (t) is the parameter. We will solve a real-life problem involving two trains departing from the same station, traveling at different speeds to determine when the second train catches up with the first. Additionally, we will sketch curves and eliminate parameters through provided examples, enhancing your understanding of parametric curves in mathematical applications.

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Understanding Parametric Equations and Curves Through Real-Life Examples

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  1. 10.1 Parametric Equations • Parametric Curve: (f(t), g(t)) • Parameter: t • x = f(t) • y = g(t)

  2. Ex 1: A cool problem! Train1 leaves the train station at noon and is traveling due east on Track #5 at 60mph. Two hours later Train2 leaves the same station and is traveling due east on Track #3 at 90mph. When does the 2nd train catch the 1st?

  3. Ex 2: Sketch the Curve & Eliminate the Parameter

  4. Ex 3: Sketch the Curve & Eliminate the Parameter x = 2 cos y = ½sin 0 ≤  ≤ 2

  5. Ex 4: Sketch the Curve & Eliminate the Parameter x = 2 cos y = sin2

  6. HW – 10.1 pg. 645 #1 – 13 odds, 22 #17 – 25 odds

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