Why parametric graphs are corrupted? - Texas Instruments TI-84 Plus Calculator

Your function is not correctly defined. If graph is function y=f(x), variable must be x; if graph is polar, variable must be theta, and if graph is parametric, variable must be t. This does not cover all possible cases. Check the graph type and the definition of the function.

In parametric functions, the variables x and y are both functions of an independent variable, called t, and that usually represents the time. The default variable in parametric functions must be called t. You can enter the limits you want. However if you type in 2 Pi it will be converted on the entry line to 6.28. The default tstep is 0.13 which is about pi/24. I fail to see what the commotion is about.
In this representation of the witch of Agnesi, the variable t is between 0 and 4Pi, and the step tstep is 0.13, a little less that pi/24
Reset your calculator and restart

That would depend on what you want to do with it. If you want to graph a polar plot, for example, you'd set it for polar plotting. If you want to graph a parametric plot instead, you'd set it for parametric plotting.

You might have used an inappropriate variable name.
For functional graphs y=F(x), the independent variable must be X
For parametric graphs, the independent variable in the x_t and y_t functions must be t.
For polar graphs the independent variable must be Theta, and for sequence graphs, it must be the special wiggly n.
Once you select the type of graph, the independent variable is entered by pressing the key marked X,T, Theta, n.

The key allows you to enter different variables, X for function graphs, T for parametric graphs, Theta for polar graphs and n fro sequence graphs.

Your calculator does not have graphing capabilities. On a graphing calculator you would first select the graph type 1. function y= f(x), 2. parametric x=x(t), y=y(t), 3.polar r=function(theta).

When you push the button [Y=] to open the function editor you will see Y1=,Y2= etc. That is the default behavior. By default the graph type is FUNCTION (y=f((x). However there are other graph types, for instance PARAM, POLAR, and SEQUENCE.
For Parametric graphs, you need two functions x as a function of t and y as a function of t. In this case, when you open the function editor, you will see pairs of functions x1(t), y1(t), x2(t), y2(t), etc. Both x and y functions of the pair must be supplied.

So if your x= function is not showing, then you must open the MODE screen, and scroll down to reach the 4th line that says FUNC, PAR, POL, SEQ. Highlight PAR and press ENTER. You do that only if you want to graph parametric functions.

When drawing function graphs of type Y1=, the name of the independent variable should be X
For polar graphs r=.., the independent variable is theta, while for parametric graphs it is T
To enter the default independent variable, press the key marked [X,Theta, T] . It will type in the correct name.

At first, you have to use t symbol for parametric functions when you operating with TI 89 Titanium. In your case you must input your relations as x1=3cos(t) and y1=2sin(2t). Then graphing it. See captured image

See carefully captured images below