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Not really a saw tooth
The sine and cosine curves don't really have a saw tooth shape. That is an artifact of the fact that we didn't compute enough points to reliablydescribe the shape of the curves. Let's improve on that.
Modify the script
Modify the code in your script to initialize the value of the variable named angInc to 45 degrees instead of 90 degrees and then load the revised version into your browser. This will cause thescript to fill in data points between the points that we already have producing the output shown in Figure 16 .
Figure 14 . Sinusoidal values at 45-degree increments. |
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Angle: -360 Sine: 0 Cosine: 1
Angle: -315 Sine: 0.71 Cosine: 0.71Angle: -270 Sine: 1 Cosine: 0
Angle: -225 Sine: 0.71 Cosine: -0.71Angle: -180 Sine: 0 Cosine: -1
Angle: -135 Sine: -0.71 Cosine: -0.71Angle: -90 Sine: -1 Cosine: 0
Angle: -45 Sine: -0.71 Cosine: 0.71Angle: 0 Sine: 0 Cosine: 1
Angle: 45 Sine: 0.71 Cosine: 0.71Angle: 90 Sine: 1 Cosine: 0
Angle: 135 Sine: 0.71 Cosine: -0.71Angle: 180 Sine: 0 Cosine: -1
Angle: 225 Sine: -0.71 Cosine: -0.71Angle: 270 Sine: -1 Cosine: 0
Angle: 315 Sine: -0.71 Cosine: 0.71Angle: 360 Sine: 0 Cosine: 1 |
Plot the new points
Every other line of text in Figure 14 should contain sine and cosine values for angles that are half way between the points that you already have plotted.Use pushpins to plot the new points and connect all of the points in each curve using rubber bands, pipe cleaners, or whatever you find most useful forthis purpose.
Same shape but shifted horizontally
The two curves still have the same shape, although shifted horizontally relative to one another and they are still periodic. However, they no longerhave a saw tooth shape. They tend to be a little more rounded near the peaks and they are beginning to provide a better representation of the actual shapes ofthe sine and cosine curves.
Let's do it again
Change the value of the variable named angInc from 45 degrees to22.5 degrees and load the new version of the html file into your browser. Now the output should look like Figure 15 .
Figure 15 . Sinusoidal values at 22.5-degree increments. |
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Angle: -360 Sine: 0 Cosine: 1
Angle: -337.5 Sine: 0.38 Cosine: 0.92Angle: -315 Sine: 0.71 Cosine: 0.71
Angle: -292.5 Sine: 0.92 Cosine: 0.38Angle: -270 Sine: 1 Cosine: 0
Angle: -247.5 Sine: 0.92 Cosine: -0.38Angle: -225 Sine: 0.71 Cosine: -0.71
Angle: -202.5 Sine: 0.38 Cosine: -0.92Angle: -180 Sine: 0 Cosine: -1
Angle: -157.5 Sine: -0.38 Cosine: -0.92Angle: -135 Sine: -0.71 Cosine: -0.71
Angle: -112.5 Sine: -0.92 Cosine: -0.38Angle: -90 Sine: -1 Cosine: 0
Angle: -67.5 Sine: -0.92 Cosine: 0.38Angle: -45 Sine: -0.71 Cosine: 0.71
Angle: -22.5 Sine: -0.38 Cosine: 0.92Angle: 0 Sine: 0 Cosine: 1
Angle: 22.5 Sine: 0.38 Cosine: 0.92Angle: 45 Sine: 0.71 Cosine: 0.71
Angle: 67.5 Sine: 0.92 Cosine: 0.38Angle: 90 Sine: 1 Cosine: 0
Angle: 112.5 Sine: 0.92 Cosine: -0.38Angle: 135 Sine: 0.71 Cosine: -0.71
Angle: 157.5 Sine: 0.38 Cosine: -0.92Angle: 180 Sine: 0 Cosine: -1
Angle: 202.5 Sine: -0.38 Cosine: -0.92Angle: 225 Sine: -0.71 Cosine: -0.71
Angle: 247.5 Sine: -0.92 Cosine: -0.38Angle: 270 Sine: -1 Cosine: 0
Angle: 292.5 Sine: -0.92 Cosine: 0.38Angle: 315 Sine: -0.71 Cosine: 0.71
Angle: 337.5 Sine: -0.38 Cosine: 0.92Angle: 360 Sine: 0 Cosine: 1 |
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