Parametric Representation of Curves - PowerPoint PPT Presentation

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Parametric Representation of Curves

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  1. Parametric Representation of Curves Lesson 9.4

  2. Parametric Representation • Define variables (x,y) to be each functions of some other variable • usually t for time • Sox = g(t) and y = h(t) • The calculator has a parametric mode

  3. Parametric Mode on Calculator • Note the appearance ofthe Y= screen • must use t • must have both a functionfor x and for y • Note also thechange in the window specs

  4. Eliminate the Parameter • Use substitution • Solve for t • Set results equalto each other • Solve for y

  5. Eliminate the Parameter • Try this one

  6. Eliminate the Parameter • Use Trig Identities • What is this figure?

  7. Eliminate the Parameter • Use other relationships: • consider y = ln x

  8. Finding Derivatives • Given x = g(t) y = h(t) • Then • Try

  9. Finding Derivatives • For… we get • To evaluate, substitute a specific t in • Also possible to eliminate the parameter with substitution

  10. Area under the Parametric Curve • Given x = x(t) y = y(t) • Then a=x(t1) b=x(t2)

  11. Area under the Parametric Curve • Try this:

  12. Assignment • Lesson 9.4 • Page 659 • Exercises:5, 9, 13, 15, 19, 23, 25, 29, 31, 33, 35, 37, 41