After you have entered the parametric equations into the TI-83 Plus graphing calculator, you can have the calculator create a table of the terms in all pairs of parametric equations in the Y= editor that are defined with a highlighted equal sign. To create a table:

1. Highlight the equal sign of those parametric equations in the Y= editor that you want to appear in the table.

Only those parametric equations in the Y= editor that are defined with a highlighted equal sign will appear in the table. To highlight or unhighlight an equal sign, press [Y=], use the

keys to place the cursor on the equal sign in the definition of either equation in the pair of parametric equations, and then press [ENTER] to toggle the equal sign between highlighted and unhighlighted.

2. Press [2nd][WINDOW] to access the Table Setup editor.

3. Enter a number in TblStart and then press [ENTER].

TblStart is the first value of the independent variable T to appear in the table.

To enter the number you have chosen for TblStart, place the cursor on the number appearing after the equal sign, press the number keys to enter your number, and then press [ENTER].

4. Enter a number in

and then press [ENTER].

gives the increment for the independent variable T. You usually want to set

equal to a small number like 0.5, 0.1, or 0.01.

To enter the number you have chosen for

place the cursor on the number appearing after the equal sign, press the number keys to enter your number, and then press [ENTER].

5. Set the mode for Indpnt and Depend.

To change the mode of either Indpnt or Depend, use the

keys to place the cursor on the desired mode, either Auto or Ask, and then press [ENTER].

To have the calculator automatically generate the table for you, put both Indpnt and Depend in Auto mode.

If you want to create a user-defined table that contains only those values of the independent variable T that you specify — and then have the calculator figure out the corresponding values of the parametric equations — put Indpnt in Ask mode and Depend in Auto mode. Step 6 explains how you construct such a table.

For a user-defined table, you don’t have to assign values to TblStart and

in the Table Setup editor.

The other combinations of mode settings for Indpnt and Depend are not that useful when you’re dealing with parametric equations.

6. Press [2nd][GRAPH] to display the table.

When you display the table, what you see on the screen depends on the modes you set for Indpnt and Depend in Step 5. And what you can do with the table also depends on these modes. Here’s what you see and what you can do:

• For an automatically generated table:

If Indpnt and Depend are both in Auto mode, then pressing [2nd][GRAPH] generates the table automatically. To display rows in the table beyond the last row on the screen, repeatedly press

until those rows appear. Likewise, repeatedly press

to display rows above the first row on the screen.

Each time the calculator redisplays a table with a different set of rows, it also automatically resets TblStart to the value of T appearing in the first row of the newly displayed table. To return the table to its original state, press [2nd][WINDOW] to access the Table Setup editor, and then change the value the calculator assigned to TblStart.

If you’re constructing a table for more than one pair of parametric equations, only the first pair will appear on the screen. To see another pair of equations, repeatedly press

until they appear. This causes the first pair of equations to disappear. To see them again, repeatedly press

until they appear.

• For a user-generated table:

If you put Indpnt in Ask mode and Depend in Auto mode so that you can generate your own table, then the table should be empty when you display it. If it’s not, clear the table.

In an empty table, key in the first value of the independent variable T you want to appear in the table, and then press [ENTER]. The corresponding values of the first pair of parametric equations automatically appear.

Key in the next value of T you want in the table and press [ENTER], and so on. The values for T that you place in the first column don’t have to be in any specific order, nor do they have to be between Tmin and Tmax.