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Figure 16 shows the output produced by this script.
| Figure 16 . Output from the code in Listing 9. |
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Start Script
adj = 3.00 opp = 4.00 unitsangle = 53.13 units
adj = -3.00 opp = 4.00 unitsangle = 126.87 units
adj = -3.00 opp = -4.00 unitsangle = 233.13 units
adj = 3.00 opp = -4.00 unitsangle = -53.13 units |
This is an issue that will become important when we reach the module that deals with vectors in all four quadrants.
Structure of the script
The script shown in Listing 9 begins by defining a function named getAngle . The purpose of this function is to return an angle in degrees in the correct quadrant based on the lengths of the adjacent and opposite sidesof an enclosing right triangle. As mentioned above, the returned angle is the angle that the hypotenuse makes with the positive horizontal axis.
An indeterminate result
The getAngle function calls the Math.atan method to compute the angle whose tangent is the ratio of the opposite side to the adjacent side of a righttriangle.
If the lengths of both the opposite and adjacent sides are zero, the ratio opposite/adjacent is indeterminate and the value of the angle cannot be computed. In fact there is noangle corresponding to the ratio 0/0. However, the function must either return the value of an angle, or must return some sort of flag indicating thatcomputation of the angle is not possible.
In this case, the function simply returns the value zero for the angle.
Avoiding division by zero
If the length of adjacent side is zero and the length of opposite side is not zero, the ratio opposite/adjacent is infinite. Therefore, the value of the angle cannot becomputed. However, in this case, the angle is known to be 90 degrees (for opposite greater than zero) or 270 degrees (-90 degrees, for opposite less thanzero). The getAngle function traps both of those cases and returns the correct angle in each case.
Correcting for the quadrant
The Math.atan method receives one parameter and it is either a positive ornegative value. If the value is positive, the method returns an angle between 0 and 90 degrees. If the value is negative, the method returns an angle between 0and -90 degrees. Thus, the angles returned by the Math.atan method always lie in the first or fourth quadrants.
(Actually, as I mentioned earlier, +90 degrees and -90 degrees are not possible because the tangent of +90 degrees or -90 degrees is an infinitelylarge positive or negative value. However, the method can handle angles that are very close to +90 or -90 degrees.)
A negative opposite/adjacent ratio
If the opposite/adjacent ratio is negative, this doesn't necessarily mean that the angle lies in the fourth quadrant. That negative ratio could resultfrom a positive value for opposite and a negative value for adjacent. In that case, the angle would lie in the second quadrant between 90 degrees and 180degrees.
The getAngle function tests the signs of the values for opposite and adjacent. If the signs indicate that the angle lies in the second quadrant, thevalue returned from the Math.atan method is corrected to place the angle in the second quadrant. The corrected angle is returned by the getAngle function.
A positive opposite/adjacent ratio
Similarly, if the opposite/adjacent ratio is positive, this doesn't necessarily mean that the angle lies in the first quadrant. That positive ratiocould result from a negative opposite value and a negative adjacent value. In that case, the angle would lie in the third quadrant between 180 degrees and 270degrees.
Again, the getAngle function tests the signs of the values for opposite and adjacent. If both values are negative, the value returned from the Math.atanmethod is corrected to place the angle in the third quadrant.
No corrections required...
Finally, if no corrections are required for the quadrant, the getAngle function returns the value returned by the Math.atan method. Note however, thatin all cases, the Math.atan method returns the angle in radians. That value is converted to degrees by the getAngle function and the returned value is indegrees.
Positive and negative angles
As you can see from the results of the test shown in Figure 16 , angles in the first, second, and third quadrants are returned as positive angles in degrees.However, angles in the fourth quadrant are returned as negative angles in degrees.
I encourage you to run the scripts that I have presented in this lesson to confirm that you get the same results. Copy the code for each script into atext file with an extension of html. Then open that file in your browser. Experiment with the code, making changes, and observing the results of your changes. Makecertain that you can explain why your changes behave as they do.
This section contains a variety of miscellaneous information.
Financial : Although the Connexions site makes it possible for you to download a PDFfile for this module at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should be aware thatsome of the HTML elements in this module may not translate well into PDF.
I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.
In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.comshowing me as the author. I neither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, pleasebe aware that it is a copy of a module that is freely available on cnx.org and that it was made and published without my prior knowledge.
Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.
-end-
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