http://www.john-weber.com/

HOW TO GRAPH PARAMETRIC EQUATIONS WITH TI89 CALCULATOR

Steps Key Sequence Screens
1. Change Graph Type to Parametric Press MODE key
  Press right arrow key
  Press 2 for parametric
2. Save New Settings Press ENTER
Let's graph the parametric equations: x = t + 2sin(2t), x = t + 2sin(5t)
3. Input Equations Press DIAMOND key, then F1 key
  type x function into xt1
  type y function into yt1
4. Graph Press F2, then 6 (for ZoomStd)
Note the direction the curve is drawn – from initial point to terminal point.
NOTE: To trace, use left/right arrow keys.
To change restrict the values of t:
5. Change Window Press DIAMOND key, then F2 (for WINDOW)
  Change appropriate values
  Press DIAMOND key, then F3 (for GRAPH)
To evaluate the equation for a particular value of t:
6. Evaluate Press F5
  Press 1 (for Value)
  Type in value for t, then ENTER
In this case, the point on the curve when t = 6 is (4.92685, 6.3085).