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Trigonometry Without Sines, Cosines, Tangents, et cetera...
Posted:
Nov 12, 2006 2:08 PM
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Last year (sophomore year in HS) I wrote a math formula for doing right triangle trigonometry with pencil and paper, eliminating the use for sines, cosine, tengents and so on as well as the use for derivatives.
I gave it to my teacher to have her check it out and I never got it back during the school year and it was her last year before retirement.
A few days ago, I decided to try and come up with the formula again, so in one of my study halls I began work on it.
After a couple days of work, I finally made the formula again.
I showed it to my Adv. Pre-Calc teacher (I had also shown the formula to him last year, as I was taking two math classes) and he said he didn't know of a formula for what I had done, so I showed it to him again and he said it worked.
In a right triangle, given acute angle x and the adjacent side a:
0.0705x+0.5774a-2.1151=b
Where b is the opposite leg
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In a right triangle, given acute angle x and opposite leg b
(0.0705x-b-2.1152)/(-0.5774)=a
Where a is the second leg
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In a right triangle, given two legs (a and b)
(0.5744a-b-2.1151)/(-0.0705)=x
Where x is the angle opposite leg b
~~
I based this off of a 30-60-90 triagle, with legs 3, sq. root of 3 and hypotenuse 2 sq. of 3.
I adjusted the 30 degree angle and saw how it affected the opposite side. I put this into the equation.
Then I did the same for when I made the second leg longer and shorter and put this change in the equation as well.
When I was done, I simplified the resultant equation and got
0.0705x+0.5774a-2.1151=b
I had a few minutes left in the study hall, so I rearranged the equation to exual x and a.
Now, obviously it isn't 100% accurate. It is 99.9999% accurate or so, though, as I rounded everything in the equation out the the ten-thousandths place.
The point of this is to make right triangle trig. doable without using sines, cosines, derivatives, tangents and so forth.
As for those of you who don't see a point as to why someone would make this: ever since I was young I have had an interest in math, and growing up I wasn't allowed to use calculators in school, so I always tried to find easier ways to do things.
If you ever wanted to do this kind of stuff without a calculator or other device of aid, you could use the above formula.
What my question is is how would I go about getting it published?
~~Christopher F. W. Edwards
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