How to Enter Polar Equations in the TI-84 Plus

The TI-84 Plus graphing calculator enables you to enter and graph polar equations. A polar coordinate system is used in Pre-calculus class as yet another way to define a point.

Changing the mode on your TI-84

You can’t begin graphing polar equations until you change the mode of your calculator. Follow these steps to change the mode of your calculator:

1. Press [MODE] and put the calculator in Polar mode.

   To highlight an item in the Mode menu, use the arrow keys to place the cursor on the item, and then press [ENTER]. Highlight POLAR in the fifth line to put the calculator in Polar mode. See the first screen.

   

   Polar equations can be graphed in Radian or Degree mode; pay attention to the problem presented and set your mode accordingly.

2. Press [2nd][ZOOM] to access your Format menu.

   Make sure the ExprOn and CoordOn are both highlighted. These settings are helpful when performing a trace on your equations.

   Your have an important decision to make! Do you want your coordinates displayed in polar form (r, θ) or rectangular form (x, y)? Choose polar form by highlighting Polar GC and pressing [ENTER] as shown is the second screen.

Selecting the graph style

All the functionality that you are used to having in Function mode is also available in Polar mode. In Polar mode, you can create graphs that look like roses, so changing the color of your graph might be important to you (especially if you want a red rose.) If you would like to customize your graph by changing the color or the line style, follow these steps:

1. Press [Y=] to access the Y= editor.

2. Press the left-arrow key to navigate your cursor to the left of the equal sign.

   See the first screen.

   

3. Press [ENTER] and use the left- and right-arrow keys to change the color using the spinner menu.

   See the second screen.

4. Press [ENTER] and use the left- and right-arrow keys to change the line style using the spinner menu.

   See the third screen.

5. Press [ENTER] twice to make the changes effective.

Entering polar equations

You may have noticed the Y= editor looks a little different than you may be used to. Y₁ has been replaced with r₁. That is not all that has changed; when you press

in Polar mode, a θ appears instead of an x.

Polar graphs take on all sorts of interesting shapes: spirals, limaçons, cardioids, lemniscates, and roses, just to name a few. These graphs are usually symmetric over the polar axis or the vertical axis.

For this exercise, use the polar equation: r = 4cos(6θ) with a range of

This polar equation forms a rose curve.

1. Press [Y=] to access the Y= editor.

2. Enter r₁ = 4cos(6è).

   Be sure to press

   

   for r. See the first screen.

   Press [ALPHA][TRACE] to access the Y-VAR menu. Your calculator has a customized Y-VAR menu so that you can save time by entering variables like r₁ or r₂ in your polar equations. See the second screen.