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xaphod

Quotes from the lighter side of life

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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? :roll:

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.

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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

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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! :roll:

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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. :roll:

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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! :roll:

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. :)

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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

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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? :roll:

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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. :roll: Best wishes Jeff

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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:

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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

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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? :roll: Jeff

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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).

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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? :roll:

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

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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

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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

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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

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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.

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hunter s. thompson once wrote: "i hate to advocate drugs, violence, or insanity to anybody, but they've always worked for me." :drinking:

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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.

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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

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