Polar coordinates r can also be used in polar

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Unformatted text preview: se functions can be called any time during a Maple session. For details about these commands, refer to the ?plot and ?plot3d help pages. Plotting Commands in Packages Many functions reside in the plots and plottools packages. These packages must be accessed by using the long or short form in the command calling sequence. For details about these packages, refer to the ?plots and ?plottools help pages. For command calling sequence information, refer to the ?UsingPackages help page. 103 104 • Chapter 5: Plotting Publishing Material with Plots Plots created with the default thickness of 0 are sometimes too faint for professionally published documents. It is recommended that you increase plot line thickness to 3 before submitting documents for professional printing. For information about this feature, see the ?plot[options] help page. 5.1 Graphing in Two Dimensions When plotting an explicit function, y = f (x), Maple requires the function and the domain. > plot( sin(x), x=-2*Pi..2*Pi ); 1 0.5 –6 –4 –2 0 –0.5 –1 2 x 4 6 Click a point in the plot window to display particular coordinates. The menus (found on the menu bar or by right-clicking the plot) allow you to modify various characteristics of the plots or use many of the plotting command options listed in the ?plot,options help page. Maple can also graph user-defined functions. > f := x -> 7*sin(x) + sin(7*x); f := x → 7 sin(x) + sin(7 x) > plot(f(x), x=0..10); 5.1 Graphing in Two Dimensions • 105 6 4 2 0 –2 –4 –6 2 4 x 6 8 10 Maple allows you to focus on a specified section in the x- and y dimensions. > plot(f(x), x=0..10, y=4..8); 8 7 y6 5 40 2 4 x 6 8 10 Maple can plot infinite domains. > plot( sin(x)/x, x=0..infinity); 0 x infinity 106 • Chapter 5: Plotting Parametric Plots You cannot specify some graphs explicitly. In other words, you cannot write the dependent variable as a function, y = f (x). For example, on a circle most x values correspond to two y values. One solution is to make both the x-coordinate and the y -coordinate functions of some parameter, for example, t. The graph generated from these functions is called a parametric plot. Use this syntax to specify parametric plots. plot( [ x-expr, y-expr, parameter =range ] ) Plot a list containing the x-expr, the y-expr, and the name and range of the parameter. For example > plot( [ t^2, t^3, t=-1..1 ] ); 1 0.5 0 –0.5 –1 0.2 0.4 0.6 0.8 1 The points (cos t, sin t) lie on a circle. > plot( [ cos(t), sin(t), t=0..2*Pi ] ); 1 0.5 –1 –0.5 –0.5 –1 0.5 1 The above plot resembles an ellipse because Maple, by default, scales the plot to fit the window. Here is the same plot again but with 5.1 Graphing in Two Dimensions • 107 scaling=constrained. To change the scaling, use the context-sensitive menu or the scaling option. > plot( [ cos(t), sin(t), t=0..2*Pi ], scaling=constrained ); 1 0.5 –1 –0.5 –0.5 –1 0.5 1 The drawback of constrained scaling is that it may obscure important details when the features in one dimension occur on a much smaller or larger scale than the others. The...
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