Trace a Parametric Graph on the TI-83 Plus

By C. C. Edwards

After you’ve graphed your parametric equations on the TI-83 Plus graphing calculator, press [TRACE] and then use the right arrow key to investigate these equations. Here’s what you see, and what you can do to change things:

  • The definition of the parametric equations: The parametric equations you’re tracing are displayed at the top of the screen, provided the calculator is in ExprOn format. If you’ve graphed more than one pair of parametric equations and you’d like to trace a different pair of equations, press


    Each time you press this key, the cursor jumps to another pair of parametric equations. Eventually it jumps back to the original pair of equations.


  • The independent variable T: The value of T corresponding to the cursor location is displayed in the lower left hand corner of the screen, provided the calculator is in CoordOn format. When you press [TRACE], the cursor is placed at the beginning of the graph of the parametric equations and T displays the value you assigned to Tmin in the Window editor. Each time you press


    the cursor moves to the next plotted point in the graph and the value of T changes to the value of the independent variable corresponding to that plotted point.

    If you press


    the cursor will move left to the previously plotted point in the graph. And if you press


    to trace a different pair of parametric equations, the calculator starts tracing that pair of equations at the value of T that was displayed on-screen before you pressed this key.

  • The values of x and y: At the bottom of the screen, you see the values of the x– and y– coordinates of the cursor location (provided the calculator is in CoordOn format). In the PolarGC format, the coordinates of this point display in polar form.

Press [CLEAR] to stop tracing the graph. Doing so also removes the name of the function and the coordinates of the cursor from the screen.

When you’re using TRACE, if you want to start tracing your parametric equations at a specific value of the independent variable T, just key in that value and press [ENTER]. (The value you assign to T must be between Tmin and Tmax; if it’s not, you will get an error message.)

After you press [ENTER], the trace cursor moves to the point on the graph corresponding to that value of T. If that point isn’t on the part of the graph that’s on-screen, you can get the cursor and the graph to appear in the same viewing window.

If the name of the parametric equations and the value of the independent variable T are interfering with your view of the graph when you use TRACE, press [WINDOW] and decrease the value of Ymin and increase the value of Ymax.