1. Parametric Equations
Lesson 10.1

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

3. Table of Values We have t as an independent variable Given
Both x and y are dependent variables
Given
x = 3t
y = t2 + 4
Complete the table t -4 -3 -2 -1 1 2 3 4 x y

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

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

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