1. Parametric Equations Lesson 10.1

2. 2 Movement of an Object Consider the position of an object as a function of time  The x coordinate is a function of time x = f(t)  The y coordinate is a function of time y = g(t) time 0

3. 3 Table of Values We have t as an independent variable  Both x and y are dependent variables Given  x = 3t  y = t 2 + 4 Complete the table t-4-3-201234 x y

4. 4 Plotting the Points Use the Data Matrix on the TI calculator Choose APPS, 6, and Current Data matrix appears  Use F1, 8 to clear previous values

5. 5 Plotting the Points Enter the values for t in Column C1 Place cursor on the C2  Enter formula for x = f(t) = 3*C1 Place cursor on the C3  Enter formula for y = g(t) = C1^2 + 4

6. 6 Plotting the Points Choose F2 Plot Setup Then F1, Define Now specify that the x values come from column 2, the y's from column 3 Press Enter to proceed

7. 7 Plotting the Points Go to the Y= screen  Clear out (or toggle off) any other functions  Choose F2, Zoom Data

8. 8 Plotting the Points Graph appears  Note that each x value is a function of t  Each y value is a function of t x = f(t) y = g(t)

9. 9 Parametric Plotting on the TI Press the Mode button  For Graph, choose Parametric Now the Y= screen will have two functions for each graph

10. 10 Parametric Plotting on the TI Remember that both x and y are functions of t Note the results when viewing the Table, ♦Y  Compare to the results in the data matrix

11. 11 Parametric Plotting on the TI Set the graphing window parameters as shown here  Note the additional specification of values for t, our new independent variable Now graph the parametric functions  Note how results coincide with our previous points

12. 12 Try These Examples See if you can also determine what the equivalent would be in y = f(x) form.  x = 2t y = 4t + 1  x = t + 5  y = 3t – 2  x = 2 cos t y = 6 cos t  x = sin 4t y = cos 2t  x = 3 sin 3 t y = cos t Which one is it?

13. 13 Assignment Lesson 10.1A Page 406 Exercises 1 – 13, odd Lesson 10.1B Page 406 Exercises 15 – 31 odd