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HP 50g Graphing Calculator - Working with Parametric Plots

Plotting on the HP 50g
The HP 50g calculator provides a host of plots to allow the user to visualize data or relationships between them. The WHITE shifted functions of the top row of keys on the HP 50g allow access to many of the input forms where plotting specifications may be entered.
Parametric plots
Parametric plots can be thought of as a plot of complex function of parameter T plotted over the complex plane. The (x,y) vector points may be used to draw the figures. Alternatively, parametric plots can be thought of as a system of two equations X=X(T) and Y=Y(T), where the Y(T) represents the imaginary part. Parametric plots can also be used to plot vertically, as an example shows.
The 2D/3D (PLOT SETUP) form
The 2D/3D (PLOT SETUP) Form is accessed from the LEFT shifted function of the key by pressing and holding down and then pressing to access . When pressed, a form is displayed with a number of choices related to plotting
Figure : Displaying plot setup form
The first choice deals with choosing the plot type. The selections for plot type are displayed by pressing , which has the label right above it. The plot types include plotting functions, polar plots, parametric plots, differential equation plots, conic plots, truth plots, histograms, bar charts, scatter charts, slopefield charts, fast 3D charts, wireframe plots, Ps-contour plots, Y-slice plots, gridmap plots, and Pr-surface plots. A CHOOSE Box appears as shown below.
Figure : Displaying the choose box
The Plot Setup form also allows the user to specify the equation being plotted if the cursor is placed on the EQ: field and the menu label is pressed – this invokes the EquationWriter to allow for the construction of the equation to be plotted. The form also allows the angle measure used and the independent variable to be specified.
  note:
The default is often 'X', but for parametric plots, this will be changed to 't').
In addition, several check boxes that are used to indicate whether the plotted points should be automatically connected together by the calculator and the horizontal and vertical tick marks used for the graph. The form also allows for the plotting of more than one function at a time.
The Y= form
The Y= form provides another way to enter your equation or function to plot. Press and hold down and then press , which is . The following form appears:
Figure : Displaying the Y form
Press with a label above it, to add a function using the equation writer.
The WIN form
The WIN form allows for the plot window specifications to be entered and changed. The lower and upper horizontal and vertical values displayed on the graph can be changed. The lower and upper value for the independent variable can also be specified on this form. To open the WIN form, press and hold down and press , which is . The following form appears:
Figure : Displaying the WIN form
The menu label will discard the results of a previous plot and the menu label will begin the plot.
Examples of parametric plotting
Example 1
Plot the equation below as a parametric plot
3 SIN( 3t ) + 2 SIN( 4t ) I
Solution
(do not forget to press AND hold the key while pressing the key)
Figure : Displaying the plot setup form
Figure : Entering the equation to be plotted
Figure : Entering the equation to be plotted
Figure : Entering the plot window specifications
Answer
The plot is displayed. A curve called lissajous figure is drawn.
Figure : Displaying the plot
To get out of the Plot Environment press
Example 2
Plot the equation below as a parametric plot.
(2*SIN(T),COS(T))
Solution
(do not forget to press AND hold the key while pressing the key)
Figure : Entering the equation to be plotted
  note:
If the calculator is in real mode then the following dialog box might appear
Figure : Checking the dialog box to set the mode
If this happens, just answer YES by pressing and proceed.
Figure : Entering the plot window specifications
Answer
The plot is displayed. An ellipse is drawn
Figure : Displaying the plot of the function
To get out of the Plot Environment press
Example 3
Plot the SIN(T) equation as a vertical plot
Solution
(do not forget to press AND hold the key while pressing the key)
Figure : Entering the equation in the plot setup
If the calculator is in real mode then a question asking if complex mode should be turned on may be displayed. Answer YES by pressing and proceed.
Figure : Entering the plot window specifications
Answer
The plot is displayed. A nice, vertical sine curve is drawn.
Figure : Displaying the plot of the function
To get out of the Plot Environment press

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