2. 10.1 Parametric Functions

3. Quick Review

4. What you’ll learn about Parametric Curves in the Plane Slope and Concavity Arc Length Cycloids Essential Questions How do we use parametric equations to define some interesting and important curves that would be difficult or impossible to define in the form y=f(x)?

5. Reviewing Some Parametric Curves 1.Sketch the parametric curve and eliminate the parametric to find an equation that relates x and y directly.

6. Reviewing Some Parametric Curves 1.Sketch the parametric curve and eliminate the parametric to find an equation that relates x and y directly.

7. Reviewing Some Parametric Curves 1.Sketch the parametric curve and eliminate the parametric to find an equation that relates x and y directly.

8. Parametric Differentiation Formulas

9. Analyzing a Parametric Curve 2.Consider the curve defined parametrically by a.Sketch a graph of the curve in the viewing window [-7, 7] by [-4, 4].

10. Analyzing a Parametric Curve 2.Consider the curve defined parametrically by b.Find the highest point on the curve. Justify your answer. Max

11. Analyzing a Parametric Curve 2.Consider the curve defined parametrically by c.Find all points of inflection on the curve. Justify your answer. Graph the function to solve.

12. Arc Length of a Parametrized Curve

13. Example Measuring a Parametric Curve 3. Find the length of the curve defined by The curve is traced once as t goes from 0 to 2 . Because of the curve’s symmetry with respect to the coordinate axis, its length is 4 times the length of the first quadrant portion. The length of the curve is 2 , which is the circumference of a circle with radius 1.

14. Cycloids 4. Find parametric equations for the path of point P in the figure above. opp. hyp. adj.

15. Pg. 535, 10.1 #1-35 odd