PJ 0 Posted June 20, 2004 For Xaphod Tan x = cos x/ sin x Sin = opposite/hypotenuse Cos = adjacent /hypotenuse Tan = opposite/adjacent If true Then the formula becomes opposite/adjacent = adjacent/hypotenuse divided by opposite/hypotenuse Invert and multiply Opposite/adjacent = adjacent/hypotenuse x hypotenuse/opposite Opposite/adjacent = adjacent/opposite where the hypotenuse cancel out. Opposite/adjacent = adjacent/opposite The formula is not true so tan x =/= cos x/sin x Pretty obvious really isn’t it? Jeff Sorry Jeff, but your formulas have errors. Here is my version with corrections in bold: Tan x = sin x / cos x Sin = opposite/hypotenuse Cos = adjacent /hypotenuse Tan = opposite/adjacent If true Then the formula becomes opposite/adjacent = opposite/hypotenuse divided by adjacent/hypotenuse Invert and multiply Opposite/adjacent = opposite/hypotenuse x hypotenuse/adjacent Opposite/adjacent = opposite/adjacent where the hypotenuse cancel out. Opposite/adjacent = opposite/adjacent The formula is true so tan x = sin x / cos x has been proven. Share this post Link to post Share on other sites

JeffM 0 Posted June 20, 2004 Sorry PJ I dont see where I am wrong. What I said also agrees with Xaph's teacher who called him a plonker for putting tanx = cosx/sinx Jeff Share this post Link to post Share on other sites

Dr. Shoe 16 Posted June 20, 2004 It's not actually as easy as that. You cannot apply the inverted fraction rule to this problem because you have x which will be a constant. In other words you MULTIPLY an angle by tan, sin and cos. i.e your "solution" implies that tan X 30 = cos X 30/sin X 30. Lets put that into figures: tan30=0.5773 (roughly) cos30=0.866 (roughly) sin30=0.5 0.866/0.5 does not equal 0.5773! (it is 1.732) Unless there is some mathematical principle I've overlook and at the risk of seeming a fool, I win I think! Share this post Link to post Share on other sites

PJ 0 Posted June 21, 2004 Sorry PJ I dont see where I am wrong. What I said also agrees with Xaph's teacher who called him a plonker for putting tanx = cosx/sinx Jeff You started out by saying that TANGENT = COSINE / SINE. This is incorrect. To make this equation true, you must invert one side of the equation. Either change TANGENT to 1 / TANGENT, or change COSINE / SINE to SINE / COSINE. The following equations are TRUE: TANGENT = SINE / COSINE 1 / TANGENT = COSINE / SINE COTANGENT = COSINE / SINE TANGENT = Opposite/Adjacent SINE = Opposite/Hypotenuse COSINE = Adjacent/Hypotenuse We can analyze the correct equation of TANGENT = SINE / COSINE this way: TANGENT = SINE / COSINE Opposite/Adjacent = Opposite/Hypotenuse divided by Adjacent/Hypotenuse Opposite/Adjacent = Opposite/Hypotenuse multiplied by Hypotenuse/Adjacent Opposite/Adjacent = Opposite/Adjacent The above equation is TRUE. I hope this helps. Share this post Link to post Share on other sites

PJ 0 Posted June 21, 2004 It's not actually as easy as that. You cannot apply the inverted fraction rule to this problem because you have x which will be a constant. In other words you MULTIPLY an angle by tan, sin and cos. i.e your "solution" implies that tan X 30 = cos X 30/sin X 30. Lets put that into figures: tan30=0.5773 (roughly) cos30=0.866 (roughly) sin30=0.5 0.866/0.5 does not equal 0.5773! (it is 1.732) Unless there is some mathematical principle I've overlook and at the risk of seeming a fool, I win I think! Dr. Shoe; The invert and multiply rule applies to all divisions involving fractions of constants and variables. Using constants and variables, here are the proofs: #1) 1/2 divided by 3/4 = 1/2 multiplied by 4/3 = 4/6 = 2/3 #2) a/b divided by c/d = a/b multiplied by d/c = ad/bc Substitute the values from #1 into #2 to see the proof. The reason why you came out with an incorrect answer is because you used an incorrect forumla. If you use the correct formula of TAN x = SIN x / COS x, you will get the correct answer. TAN 30 = .5773 COS 30 = .866 SIN 30 = .5 TAN 30 = SIN 30 / COS 30 .5773 = .5 / .866 .5773 = .5773 See my explanation in the previous posting to JeffM for further info. I hope this helps. Share this post Link to post Share on other sites

JeffM 0 Posted June 21, 2004 PJ I still dont see what I said was wrong. What you did was prove that tanx=sinx/cosx Xaph's teacher told him in her way that tanx=cosx/sinx was incorrect. I set out to prove it was correct and as you can see at the end I said that tanx=/=cosx/sinx therefore proved the equation incorrect. Jeff Share this post Link to post Share on other sites

PJ 0 Posted June 21, 2004 PJ I still dont see what I said was wrong. What you did was prove that tanx=sinx/cosx Xaph's teacher told him in her way that tanx=cosx/sinx was incorrect. I set out to prove it was correct and as you can see at the end I said that tanx=/=cosx/sinx therefore proved the equation incorrect. Jeff Sorry JeffM for misunderstanding your posting. Silly me. We are both trying to prove the same thing but going at it from opposite ends. Enough said ..... say no more .... nudge nudge ..... no what I mean? Share this post Link to post Share on other sites

JeffM 0 Posted June 21, 2004 PJ, PJ you know you are only allowed two mistakes a year then you get the sack. I trust that this one is your first but please be careful there is another 6 months or so left in the year We wouldnt want to loose you. Hope the rest of your week is better. Best wishes Jeff Share this post Link to post Share on other sites

Dr. Shoe 16 Posted June 21, 2004 Dr. Shoe; The invert and multiply rule applies to all divisions involving fractions of constants and variables. Using constants and variables, here are the proofs: #1) 1/2 divided by 3/4 = 1/2 multiplied by 4/3 = 4/6 = 2/3 #2) a/b divided by c/d = a/b multiplied by d/c = ad/bc Substitute the values from #1 into #2 to see the proof. The reason why you came out with an incorrect answer is because you used an incorrect forumla. If you use the correct formula of TAN x = SIN x / COS x, you will get the correct answer. TAN 30 = .5773 COS 30 = .866 SIN 30 = .5 TAN 30 = SIN 30 / COS 30 .5773 = .5 / .866 .5773 = .5773 See my explanation in the previous posting to JeffM for further info. I hope this helps. Yes I know that! It's just that I was trying to prove that Xaphod's teacher was right to call him a plonker! :rofl: Share this post Link to post Share on other sites

JeffM 0 Posted June 22, 2004 Exactly what I was trying to prove, that Xaph was a plonker (what ever that is) Sorry Xaph. All in fun. Jeff Share this post Link to post Share on other sites

xaphod 2 Posted June 22, 2004 Hi, JeffM, A plonker in UK-speak is a particular variety of idiot. It's very embarassing when a gorgeous blonde .... with brains .... puts down a fairly bright lad who can't be bothered to learn his trigonometrical identities. Auntie Babs must have been a good teacher, though. She helped me get an A grade .... who says sex only sells ! Perhaps it's time I started a mathematical thread ???? Xa Share this post Link to post Share on other sites

JeffM 0 Posted June 22, 2004 Got you now Xaph. Plonker:- some one who looks at Auntie Babs all the time instead of his maths paper, who is intensely interested in what is happening at the front of the class (and it has nothing to do with what is on the blackboard) who makes himself the center of attention by writing down incorrect equations. Have I got it right? Jeff Share this post Link to post Share on other sites

Dr. Shoe 16 Posted June 22, 2004 Sounds like it! I was a plonker for most of my 5th form year! Miss Duvall (devastating knee boots), Mrs Sillitoe (v nice), Miss Price (gym teacher, fit in every possible meaning of the word). Share this post Link to post Share on other sites

xaphod 2 Posted June 24, 2004 Got you now Xaph. ..... who is intensely interested in what is happening at the front of the class (and it has nothing to do with what is on the blackboard) .... who makes himself the center of attention by writing down incorrect equations. Have I got it right? Jeff You have to remember this was in the time of the miniskirt, so when Babs reached up to write at the top of the board, the sight made one's eyes sore. Funnily enough, I used to sit in the front of the class for maths. The bit about attention grabbing .... could be .... however I remember one St David's day, the Welshman in the class wore a leek (sortof onion) in his top pocket, so I wore my dad's old wartime gas-mask ! Xa Share this post Link to post Share on other sites

shyguy 1 Posted September 10, 2004 In a follow up, mankind is working at making more things idiotproof, while nature is throwing up ever more resourceful idiots to maintain the status quo Share this post Link to post Share on other sites

xaphod 2 Posted September 13, 2004 In a follow up, mankind is working at making more things idiotproof, while nature is throwing up ever more resourceful idiots to maintain the status quo Very true SG .... here's a corollary .... I've forgotten where I found the quote The total amount of intelligence on the planet is a constant ..... .... pity, the population is increasing. Xa Share this post Link to post Share on other sites

xaphod 2 Posted November 18, 2004 The first recorded reference to the county of Nottinghamshire was in 1016 as Snotingahamscir .... meaning the shire around the dwelling (ham) of the followers of Snot, a Norseman. . . . . . . . .... for non-native English speakers, snot is also slang for that green stuff that runs from your nose when you have a cold ! Xa Share this post Link to post Share on other sites

Dr. Shoe 16 Posted November 18, 2004 Actually, I think you'll find that he invented the stuff and that it was named in his honour! :rofl: Share this post Link to post Share on other sites

genebujold 0 Posted November 19, 2004 The total amount of intelligence on the planet is a constant ..... .... pity, the population is increasing. Xa Woah! A sign of intelligence! As Henry said, "Damn the torpedos!" I, for one, thank God that the repositories of information throughout our world is widespread, at the very least, and very well widespread, at most. It's good to know our collective wit and wisdom are being dissemenation, usually after little more than a contrary event, prior to allowing the attention of the soldiers to descend upon the probelm at hand. God bless, and good night. Share this post Link to post Share on other sites

r1g0r 0 Posted November 29, 2004 hunter s. thompson once wrote: "i hate to advocate drugs, violence, or insanity to anybody, but they've always worked for me." :drinking: Share this post Link to post Share on other sites

xaphod 2 Posted January 4, 2005 Woah! A sign of intelligence! As Henry said, "Damn the torpedos!" I, for one, thank God that the repositories of information throughout our world is widespread, at the very least, and very well widespread, at most. It's good to know our collective wit and wisdom are being dissemenation, usually after little more than a contrary event, prior to allowing the attention of the soldiers to descend upon the probelm at hand. God bless, and good night. One scary fact about World population .... When my dad was born there were one and some billion people on the planet. When he was a young man it hit 2 billion. When I was a boy, we had got to 3. It's well on it's way to 4 now, and by the time I'm shoving up the daisies, it is projected to be 5 billion, all of whom will want to live in warm houses, be adequately fed, drive cars, absorb resources, contribute to Global Warming and the Global garbage pile. ..... sorry guys, something has got to give. Xa Checked my data, hence the edit. Share this post Link to post Share on other sites

xaphod 2 Posted January 4, 2005 and less doom and gloom .... It seems that the Royal Automobile Club breakdown patrols have some really wierd problems to fix at times. It is not unknown for teething children to chew on car key fobs and swallow the immobiliser transponder chip they contain. The breakdown guys fix this by holding the offending infant close to the ignition while the key is operated as normal. Xa Share this post Link to post Share on other sites