1. 10.1 Parametric Functions

2. Quick Review

3. 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)?

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

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

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

7. Parametric Differentiation Formulas

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

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

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

11. Arc Length of a Parametrized Curve

12. 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 2p. 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 2p, which is the circumference of a circle with radius 1.

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

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