Before graphing a polar graph, you need to set the window of your TI-84 Plus calculator. If your graph seems incomplete, it is probably due to the way you set your window variables. The variables that tend to cause problems are θmin, θmax, and θstep.
The range given in this problem is
It is easy to see that θmin=0 and θmax=2π. Even though these variables are part of the Window editor, they don’t actually affect the viewing window of the graph on your calculator. You would have to change the minimum and maximum values of X and Y to change the graphing window. Does that seem strange? Maybe this explanation will help.
In Function mode, piecewise functions have a restricted domain so that you can only see a "piece" of the function. In Polar mode, the range can be restricted, which can make it difficult to predict what the "whole" graph would look like if the θ values were not restricted to a certain interval. As a general rule of thumb, you should be able to see the whole graph if
in Radian mode, or
in Degree mode.
θstep is the increment between θ values. When you graph a polar equation, your calculator evaluates r for each value of θ by increments of θstep to plot each point. Be careful! If you choose a θstep that is too large, your polar graph will not be accurate. If you choose a θstep that is too small, it will take a long time for your calculator to graph.
In the ZStandard window, the default value for θstep is π/24 in Radian mode or 15 in Degree mode. In most cases, this is a good balance between graphing accuracy and the time it takes to graph.
Follow these steps to set the window for a Polar graph:
Press [WNDOW] to access the Window editor.
See the first screen.
Change the value of èmin, èmax, and èstep.
Enter 2π for θmax, and press [ENTER]. Enter π/24 for θstep, and do not press [ENTER] as shown in the second screen.
Press [ENTER].
Notice, pressing [ENTER] evaluates π/24 and the approximate value of 0.13089969389958 is displayed. See the third screen.