After you’ve graphed your polar equations on the TI-83 Plus graphing calculator, you can use the calculator to trace the polar graph. Press [TRACE] and then use

to investigate these equations. Here’s what you will see, and what you can do to change things:

• The definition of the polar equation: The polar equation you’re tracing is displayed at the top of the screen, provided the calculator is in ExprOn format. If you have graphed more than one polar equation and you would like to trace a different equation, press

Each time you press this key, the cursor jumps to another polar equation. Eventually it jumps back to the original equation.

• The independent variable

The value of

corresponding to the cursor location is displayed in the lower- left corner of the screen, provided the calculator is in CoordOn format. When you press [TRACE], the cursor is then placed at the beginning of the graph of the polar equation and

displays the value you assigned to

in the Window editor. Each time you press

the cursor moves to the next plotted point in the graph and the value of

changes to the value of the independent variable corresponding to that plotted point.

If you press

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

to trace a different polar equation, the tracing of that equation will start at the same value of

that was displayed on the 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 RectGC and CoordOn format. In the PolarGC format, the coordinates of this point display in polar form.

Press [CLEAR] to terminate tracing the graph. This also removes the name of the function and the coordinates of the cursor from the screen.

If you’re using TRACE and you want to start tracing your polar equation at a specific value of the independent variable

just key in that value and press [ENTER]. (The value you assign to

must be between

and

if it isn’t, 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

If that point is not on the part of the graph appearing on the screen, you can get the cursor and the graph in the same viewing window.

If the name of the polar equation and the value of the independent variable

are interfering with your view of the graph when you use TRACE, increase the height of the window by pressing p and decreasing the value of Ymin and increasing the value of Ymax.