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Trigonometry Without Sines, Cosines, Tangents, et cetera...
Posted:
Nov 12, 2006 2:08 PM


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. PreCalc 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+0.5774a2.1151=b Where b is the opposite leg ~~ In a right triangle, given acute angle x and opposite leg b
(0.0705xb2.1152)/(0.5774)=a Where a is the second leg ~~ In a right triangle, given two legs (a and b)
(0.5744ab2.1151)/(0.0705)=x Where x is the angle opposite leg b ~~ I based this off of a 306090 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+0.5774a2.1151=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 tenthousandths 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



