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A lot of data points
Once again, every other line of text in Figure 15 contains new sine and cosine values for angles that you don't have plotted yet.
Plotting all of these point is going to require a lot of pushpins and a lot of effort. Before you do that, let's think about it.
Two full cycles
You should have been able to discern by now that your plots for the sine and cosine graphs each contain two full cycles. An important thing aboutperiodic functions is that once you know the shape of the curve for any one cycle, you know the shape of the curve for every cycle from minus infinity to infinity. Theshape of every cycle is exactly the same as the shape of every other cycle.
Saving pushpins and effort
If you are running out of pushpins or running out of patience, you might consider updating your plots for only one cycle.
You should be able to discern that your curves no longer have a saw tooth shape. Each time we have run the script, we have sampledthe amplitude values of each curve at twice as many points as before. Therefore, the curves should be taking on a smoother rounded shape that is betterrepresentation of the actual shape of the curves.
Continue the process
You can continue this process of improving the curves for as long as you have the graph board space, pushpins, and patience to do so. Just divide the value of the variable named angInc by a factor of two and rerun the script. That will produce twice as many data points that are only half as far apart on thehorizontal axis.
If you choose to do so, you can plot only the new points in one-half of a cycle to get an idea of the shape. By now you should have discerned that each half of a cycle has the same shape, only onehalf is above the horizontal axis and the other half is a mirror image below the axis.
Plot of cosine and sine curves
Getting back to tactile graphics, for the benefit of any sighted person that may be assisting you, Figure 16 shows a cosine curve plotted above a sine curve very similar to the curves that you have plotted on your graph board.( Figure 16 shows a mirror image of the actual curves because the file named Phy1020a1.svg is intended to be used for manual embossing from the back of thepaper.) A non-mirror-image version is shown in Figure 20 .
Figure 16 . Mirror image plot of cosine and sine curves from the file named Phy1020a1svg. |
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This image contains lines that aren't straight, but with a little care, your assistant should be able to do a reasonably good job of embossing them whenthe image is printed as the full 8.5x11 inch version.
Page setup
If you use the IVEO Viewer to print the file named Phy1020a1.svg, you should use the default Page Setup selection for Letter (Landscape).
Grid lines
The image in Figure 16 contains 7 vertical grid lines. The vertical grid line in the center represents an angle of zero degrees. The space between each gridline on either side of the center represents an angle of 90 degrees or PI/2 radians.
There are two horizontal grid lines. One is one-fourth of the way down from the top. The other is one-fourth of the way up from the bottom.
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