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Sinusoidal amplitude versus angle
Please copy the code from Listing 8 into an html file and open the file in your browser.
| Listing 8 . Sinusoidal amplitude versus angle. |
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<;!-- File JavaScriptZZ.html --><;html><;body><;script language="JavaScript1.3">function toRadians(degrees){
return degrees*Math.PI/180}//end function toRadians
//============================================//function toDegrees(radians){
return radians*180/Math.PI}//end function toDegrees
//============================================//var angInc = 90
var angStart = -360var ang = angStart
var angEnd = 360var sine
var cosinewhile(ang<;= angEnd){
//Compute sine and cosine of anglesine = Math.sin(toRadians(ang))
cosine = Math.cos(toRadians(ang))//Reduce the number of digits in the outputsine = (Math.round(100*sine))/100
cosine = (Math.round(100*cosine))/100//Display the resultsdocument.write("Angle: " + ang +
" Sine: " + sine +" Cosine: " + cosine +
"<;/br>")//Increase the angle for next iteration
ang = ang + angInc}//end while loop<;/script><;/body><;/html> |
Output from the script
When you open your html file in your browser, the output shown in Figure 13 should appear in your browser window.
| Figure 13 . Sinusoidal values at 90-degree increments. |
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Angle: -360 Sine: 0 Cosine: 1
Angle: -270 Sine: 1 Cosine: 0Angle: -180 Sine: 0 Cosine: -1
Angle: -90 Sine: -1 Cosine: 0Angle: 0 Sine: 0 Cosine: 1
Angle: 90 Sine: 1 Cosine: 0Angle: 180 Sine: 0 Cosine: -1
Angle: 270 Sine: -1 Cosine: 0Angle: 360 Sine: 0 Cosine: 1 |
Figure 13 contains the data for two different curves. One is a sine curve and the other is a cosine curve.
Plot the points using pushpins
You should be able to plots these data values as two separate curves on your graph board by inserting pushpins at the coordinate values shown and thenconnecting the pushpins with rubber bands, pipe cleaners, yarn, flexible wire, or something similar. (Rubber bands might not work if you are using a homemadeplot board constructed from Styrofoam, because the pins pull too easily.)
Remember, the angle values from -360 degrees (-2*PI radians) to +360 degrees (+2*PI radians) are horizontal coordinates while the correspondingvalues for the sine and cosine are vertical coordinates.
Saw tooth curves
Once you have plotted the points, you should be able to discern two curves, each of which is a saw tooth.
The two curves have exactly the same shape, but one is shifted horizontally relative to the other. For example, the sine curve has a value of zero at anangle of zero (the origin) and it is asymmetric about the vertical axis.
The cosine curve, on the other hand has a value of 1 at an angle of zero and it is symmetric about the vertical axis.
Periodic curves
These are periodic curves. For example, the shape of the sine curve between -360 and 0 is the same as the shape of the sine curve between 0 and +360. Eachof those ranges represents one cycle of the periodic curve.
We only computed the values from -360 to +360. However, if we had computed the values from -3600 to + 3600, the overall shape of the curve would not differfrom what we have here. The shape of each cycle of the curve would be identical to the shape of the cycle to the left and the cycle to the right.
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