### Author Topic: ATN, a small correction  (Read 1038 times)

#### Ginuzz

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##### ATN, a small correction
« on: November 19, 2011, 02:30:46 PM »
The definition of ATN, the arctan, as given in WIKI is mistaken.  The arctan of an angle makes little sense, for the arctan IS an angle.  What it tells you is the angle whose tangent you give it.  For instance, pi/4 (or 45 deg) is the angle whose tangent is 1.  The definition should read "Returns the angle, in radians, whose tangent is n."

#### Mrwhy

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##### Re: ATN, a small correction
« Reply #1 on: November 20, 2011, 12:23:10 AM »
WELL SAID Ginuzz
These errors, noticed by the painstaking learner, make QB 64 very hard to understand.
They drive away the very people who if they join us will most bebefit QB64

#### Clippy

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• I LOVE π = 4 * ATN(1)    Use the QB64 WIKI >>>
##### Re: ATN, a small correction
« Reply #2 on: November 20, 2011, 03:48:49 AM »
This is what is says in Qbasic:

Quote
ATN - a math function that returns the arctangent of a numeric expression (the angle whose tangent is equal to the numeric expression)
Does that make it any clearer? For obvious reasons we cannot quote that.
« Last Edit: November 20, 2011, 03:59:46 AM by Clippy »
QB64 WIKI: Main Page

#### OlDosLover

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##### Re: ATN, a small correction
« Reply #3 on: November 20, 2011, 04:16:58 AM »
Hi all,
Ok i feel im qualified to comment on this subject. Im a maths dummy and so i go off the definition. An example given does me no good unless i understand the definition. And hence we have several definitions.
Quote
The arctan of an angle makes little sense, for the arctan IS an angle.  What it tells you is the angle whose tangent you give it.
Quote
ATN - a math function that returns the arctangent of a numeric expression (the angle whose tangent is equal to the numeric expression)
Now no offence but in particular this part of the description does give me a mental image to help explain it.
Quote
(the angle whose tangent is equal to the numeric expression)
The reason i understand this bit of the snippet is that i understand Tangent. Now
Quote
the angle whose tangent you give it
is pretty much the same in my book.
As NONE of you have any idea of whats in my head HOW can you decide that one description is better or worse than another? Thank you all for the descriptions i really do appreciate the knowledge.
OlDosLover.

#### Clippy

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• I LOVE π = 4 * ATN(1)    Use the QB64 WIKI >>>
##### Re: ATN, a small correction
« Reply #4 on: November 20, 2011, 05:46:50 AM »
Well it sort of inherited the idea that the value was expressed in radians like SIN and COS, when it was not actually a radian value. I added some examples to make it clearer. Tangent values are not measured in radians. It is a ratio of SIN to COS.

http://qb64.net/wiki/index.php?title=ATN
QB64 WIKI: Main Page

#### Mrwhy

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##### Re: ATN, a small correction
« Reply #5 on: November 20, 2011, 06:41:37 AM »
Oldos, there are at LEAST 3 things
Thinking I know the general idea
Thinking I know exactly (definition)
Thinking I understand

For me the general idea is all I can ever hope for and I genuinely believe that ONLY EXAMPLES teach us anything at all! It's how we learned to walk; how we learned to talk.

An easy way to get the general idea comes in two steps
(a) Draw a triangle and POINT OUT which two sides have length-ratio that equals "tangent" and which ANGLE it is the tangent of.
(b) REMEMBER, from your experience so far, that it is USEFUL to have things "the other way round".
For example if you know y only when we know x, then the "other way round" is useful when we DO KNOW y but want to know x.  For example when y=x+4 then x=y-4  "turns it around"
When y=x squared, then x=sqrt(y).  When y= tan(x) then x= atn(y)

AFTER I get the general idea, THEN is the time to think whether atn might have MANY values for each given y

For what you want is a rough definition and maths folk have no interest in helping you find that.
They will tell you that tan(x) = [exp(ix)-exp(-ix)]/[i*(exp(ix)+exp(-ix))]
and yes, "turn that around to give x" and you get logarithms

Clippy's tangent is a good way, but suffers from the fact that to "see what" tangent is you have to see what BOTH sine and cosine are before "dividing one by the other" is much help!
« Last Edit: November 20, 2011, 07:50:51 PM by Mrwhy »

#### Clippy

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• I LOVE π = 4 * ATN(1)    Use the QB64 WIKI >>>
##### Re: ATN, a small correction
« Reply #6 on: November 20, 2011, 06:44:46 AM »
That is why they are LINKED! Crayons anyone?

I am not gonna teach TRIG on every page just because you don't wanna look...
QB64 WIKI: Main Page

#### OlDosLover

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##### Re: ATN, a small correction
« Reply #7 on: November 20, 2011, 07:11:35 AM »
Hi all,
Well i spose that different people learn different ways like concept verses example. I find visual images the best way for me personally to grasp the idea of what it does. Weather i understand how or why it works is not so important to me.

Quote
For what you want is a rough definition and maths folk have no interest in helping you find that.
They will tell you that tan(x) = [exp(ix)-exp(-ix)]/[2i*(exp(ix)+exp(-ix))]
The wiki has to have a "level" at where it stops. It is up to the reader to research more needed knowledge to be able to competently use it in my opinion. To get everyone to agree on that "level" would be a nightmare. As a maths illiterate i need to research the names (descriptive labels) used to apply the explanation so i am thinking about the same thing that the author is describing. Minds use different choices of words and sentence structure to describe  what it is that is envisioned as writing occurs. I see it as my responsibility to be able to interpret what the author means by his words.
OlDosLover.

#### Ginuzz

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##### Re: ATN, a small correction
« Reply #8 on: November 20, 2011, 08:18:04 PM »
Who would have suspected that such a small correction could stir up such contentious discussion.  My point was that what it said in WIKI was incorrect and confusing.  The way I see it is this: if you are using arctan in a program you must know what it is (with one exception*).  What you need to know is how say it in the programming language.  It would be enough to tell you that in QB, whatever version you're using, arctan is written ATN.  To use the words "the angle whose tangent is..." rather than "arctan" is a little more elaborate.  But QB is not the place to DEFINE the trigonometric functions any more than it is the place to define the square root.  It seems to me also that the purpose of this forum is not to decide how best to teach or learn trigonometry any more than it is the place to decide who wrote Shakespeare's plays, no matter how much fun that may be.
* The exception: in QB, probably the simplest way to write pi is 4*ATN(1).  You don't really need to know why.

#### DarthWho

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##### Re: ATN, a small correction
« Reply #9 on: November 20, 2011, 10:42:09 PM »
thanks a lot for stereotyping mathematicians MrWhy (in my case I am an Undergraduate physicist with a bent toward abstract mathematics [so I am a physicist and a mathematician]) I happen to take pains to clarify a statement when others do not comprehend it.

a definition is very helpful to give an example the Dirac delta function is defined such that: everywhere except at 0 δ(x)=0 at δ(0)=∞ such that the area under the curve = 1 now this partial definition may not seem like the area under δ(x) and 2*δ(x) is the same but this is not true the definition goes on to stipulate that the formula k*δ(x) multiplies the area under the curve rather than the value of the curve itself. (after all 2*∞=∞ but 2*3=6)

if anyone needs further explanation of that just ask.

PS your formula there is equal to tan(x)/2 not tan(x)...
Rassilon: My lord Doctor; My lord Master; My lord DarthWho
The Doctor and the master at the same time :WHAT!?!?!

FastMath 1.1.0 released: http://dl.dropbox.com/u/12359848/fastmath.h

#### Clippy

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• I LOVE π = 4 * ATN(1)    Use the QB64 WIKI >>>
##### Re: ATN, a small correction
« Reply #10 on: November 21, 2011, 12:36:25 AM »
I just would categorize Mr.Why as an incorrigible wonderer... or is it wanderer...
QB64 WIKI: Main Page

#### OlDosLover

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##### Re: ATN, a small correction
« Reply #11 on: November 21, 2011, 07:25:31 AM »
Hi all,

Quote
Who would have suspected that such a small correction could stir up such contentious discussion.  My point was that what it said in WIKI was incorrect and confusing.  The way I see it is this:
Discussion is healthy and needed. I respect your answer Ginuzz. Interpretation by nature is subjective and there may be many different meanings arrived at by many people. Who is right and who is wrong? That i believe can not be answered absolutely.
You are right to bring this to discussion. Would it be possible to ALL agree on one answer? Probably not. The wiki is based off the old QBasic help explanations (guideline).
Quote
For me the general idea is all I can ever hope for and I genuinely believe that ONLY EXAMPLES teach us anything at all! It's how we learned to walk; how we learned to talk.
This i respectfully disagree with. NOT everything fits into this category and as such we need to approach new learning with open minds believing that anything is possible. Now all im doing is offering another (differing) interpretation if you see my point.
OlDosLover.

#### DarthWho

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##### Re: ATN, a small correction
« Reply #12 on: November 21, 2011, 10:25:02 AM »
I have to concur with OlDos on both points in that last post of his; as long as it doesn't become a flame war discussion is healthy  opposing sides act as the devils advocate for the other side allowing both sides viewpoints to evolve hopefully toward better comprehension of the subject.

Mrwhy if your statement were the case there would not be any spontaneous insights on anything an therefore no great scientfic discoveries would be made.
Rassilon: My lord Doctor; My lord Master; My lord DarthWho
The Doctor and the master at the same time :WHAT!?!?!

FastMath 1.1.0 released: http://dl.dropbox.com/u/12359848/fastmath.h

#### Mrwhy

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• My Dad called me Mr Why when I was 5.
##### Re: ATN, a small correction
« Reply #13 on: November 21, 2011, 11:45:00 AM »

your formula there is equal to tan(x)/2 not tan(x)...

Thanks for noticing my typo (already corrected) - thanks for even caring

#### DarthWho

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##### Re: ATN, a small correction
« Reply #14 on: November 21, 2011, 12:11:51 PM »
you are welcome I just noticed something odd plotted it mentally and then checked it on paper and found that it was definitely incorrect so I corrected the minor problem
Rassilon: My lord Doctor; My lord Master; My lord DarthWho
The Doctor and the master at the same time :WHAT!?!?!

FastMath 1.1.0 released: http://dl.dropbox.com/u/12359848/fastmath.h