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How do I make a graph of a circle? |
  
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How do I make a graph of a circle? |
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The Y=f(X) command will only generate data points for which there is one unique Y value for every X. So even though Y=sqrt(R^2-X^2) is the correct equation for a circle, use of this equation with Y=f(X) will only result in a semicircle (the positive Y half). But don't despair; generating a circle is no problem with X=f(T), Y=g(T). With T varying from 0 to 360 degrees, X=R*cos(T), Y=R*sin(T) defines a circle of radius R (substitute the actual radius for "R") centered at the origin. Of course if you want a circle centered at (H,K), you'd use X=H+R*cos(T) and Y=K+R*sin(T).
Initially the physical dimensions of your circle will most likely not be circular, depending on the window size. That's simply because by default, DPlot uses as much of the display monitor as possible to plot your data. You can force circular circles by using the Extents/Intervals/Size command on the Options menu and specifying equal extents for the X and Y axes and equal physical dimensions (check "Specify plot size" and enter equal values for the plot width and height). Alternatively, after checking both the "Specify extents" and "Specify plot size" boxes, click the "Set X:Y=1:1" button.
The X=f(T), Y=g(T) command is of course useful for other geometric shapes that have more than one Y value for each X. To plot an ellipse X^2/A^2 + Y^2/B^2 = 1, for example, use X=A*cos(T), Y=B*sin(T) with, again, T varying from 0 to 360 degrees.
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