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Topic: Algebra help needed badly.

dis0rderd
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posted February 10, 2005 19:01
Hey, this is my first day, so im not really sure where to put it, so i figured the math forum would fit well.
I have a math question and if anyone could help me.
You know cos A= adj/hyp. If you let A be any angle between 0 and 90 degrees, you would notice that cos A is always between 0 and 1. Explain why cos A is always between 0 and 1.
If someone could help me, that would be so wonderful..
thanks guys.
Posts: 10  From: red deer  Registered: Feb 2005
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Alan!
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posted February 10, 2005 20:29
actually, algebra and particularly its relation to geometry and angles may come in quite useful here.
*alan begins constructing shelter*
okay, you're going to need a solid foundation, probably a big wooden box. or steel? you want steel? okay, faraday we can do. hold this...
now lets cover the whole lot in black plastic. good good. now just sit there and wait...
 Alan!
Two rabbis, a priest, and an awkward silence after there's no intelligible punch line to this joke, walk into a bar.
Posts: 219  From: Perth, Western Australia  Registered: Apr 2002
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Rhonwyyn
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posted February 10, 2005 20:39
Hey, I was pretty impressed with my (rather skillful) answer in the other thread where this random person queried the same question.
No one noticed.
:pout:
 Change the way you SEE, not the way you LOOK!
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TheMoMan
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posted February 11, 2005 05:21
Rhonwyyn _______I think that the problem with Mathmatics in this country is that the texts don't teach theory of math any more just give them the formula and hope for the best. Now for TheMoMans method.
Get a piece of graph paper, near the center draow a dot now pick some scale say ten squares to the inch. Now draw a circle from that dot with a ten square radius.
Now you have a nice circle drawn on the paper, draw two lines one horizontal(flat) and one vertical(up and down) through the center, you should have a circle that looks like you are looking through a gun sight..
Now the flat line(horizontal ) represents the values of the Cosine and the vertical line reprents the values of the Sine. Notice that all values of X and Y must be contained by the circle as you pass around it, so they must be less than unity (one to  one).
If you imagine a line at 45 degrees you will see that it is almost eight squares out and eight squares up (.707 actually)
dis0rderd Can you see the Concept NOW!
 Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.
Benjamin Franklin,
Posts: 5848  From: Just South of the Huron National Forest, in the water shed of the Rifle River  Registered: Sep 2002
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drunkennewfiemidget
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posted February 11, 2005 06:51
quote: Originally posted by TheMoMan: Rhonwyyn _______I think that the problem with Mathmatics in this country is that the texts don't teach theory of math any more just give them the formula and hope for the best. Now for TheMoMans method.
Get a piece of graph paper, near the center draow a dot now pick some scale say ten squares to the inch. Now draw a circle from that dot with a ten square radius.
Now you have a nice circle drawn on the paper, draw two lines one horizontal(flat) and one vertical(up and down) through the center, you should have a circle that looks like you are looking through a gun sight..
Now the flat line(horizontal ) represents the values of the Cosine and the vertical line reprents the values of the Sine. Notice that all values of X and Y must be contained by the circle as you pass around it, so they must be less than unity (one to  one).
If you imagine a line at 45 degrees you will see that it is almost eight squares out and eight squares up (.707 actually)
dis0rderd Can you see the Concept NOW!
... wow. I have written software that used sine and cosine to cause movement and judge bounce angles, etc.
I have done this sort of thing in class.
I honest to God just learned more from that post than I did in most math classes, because until now, COS was just a button a computer calculated or a calculator did for me. Now I understand what it means.
Thanks, sir.
(I'm dead serious, not joking.)
Posts: 4897  From: Cambridge, ON, Canada  Registered: Jun 2004
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magefile
Highlie
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posted February 11, 2005 08:20
The unit circle is indeed the key to understanding trig. Unfortunately, they don't seem to teach it in HS anymore.
 Let them be stupid  the market will sort it out.
Posts: 743  From: Massachusetts  Registered: Aug 2004
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Cap'n Vic
Member # 1477

posted February 11, 2005 08:56
Good shit mo man!!
Like the newf, that blew my mind. You should have been a math teacher.
 (!) (T) = 8D
Posts: 5471  From: One of the drones from sector 7G  Registered: Jun 2002
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TheMoMan
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posted February 11, 2005 13:11
Thank You My August forum members, that is about the easyest way to explain the concept in 2D it gets more complicated when you have to deal with that pesky third axis. When writing NC code for machine tools you also have a set of I,J,K deminsions to tell the machine where the center of an arc is, it gets real tricky if the machine does not have a canned helix program that you can just tell it the helix def.
 Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.
Benjamin Franklin,
Posts: 5848  From: Just South of the Huron National Forest, in the water shed of the Rifle River  Registered: Sep 2002
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TheMoMan
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posted February 11, 2005 15:00
Sorry about the double post but I just realized how much Math I learned over the past thirty years of Machine building.
To be truthfull I failed solid geometry and anilitical algebra in my senior year of high school, I then had terible luck at college level until, I came home from the service and attended Michigan State University, where I met a Grad Student,Math instructor that taught his students to find the solution. He did not teach us formulas or do this and you will get the result, it was taught as a history class in math from this can you calculate the solution.
I gues he did well I can do sperical geometry and keep the cutting tool axis perpendicular to the surface to be machined, hey not bad for a math failure.
No wonder the apprentices always came to me for their math problems.
 Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.
Benjamin Franklin,
Posts: 5848  From: Just South of the Huron National Forest, in the water shed of the Rifle River  Registered: Sep 2002
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Luxxie
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posted March 02, 2005 21:48
I really appreciate your detailed answer, TheMoMan. I tend to get too caught up in the formulas used to solve problems or to program, and fail to think about the theories behind the concept. I find that I learn so much more thoroughly when the theory of a concept is learned, not just the formula memorized.
I agree, you should have been a teacher!
 I beat the internet; the end guy was hard!
Posts: 10  From: Neverland  Registered: Mar 2005
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drunkennewfiemidget
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posted March 03, 2005 05:18
quote: Originally posted by Luxxie: I really appreciate your detailed answer, TheMoMan. I tend to get too caught up in the formulas used to solve problems or to program, and fail to think about the theories behind the concept. I find that I learn so much more thoroughly when the theory of a concept is learned, not just the formula memorized.
I agree, you should have been a teacher!
Definitely. I went through highschool up until OAC (grade 13 in Ontario that once existed) Finite. I also took grade 13 algebra/geometry, and grace 13 calculus. NONE of those courses told me how cosine worked beyond hitting a button on a calculator. If I was taught that one simple theory that mr moman pointed out in 1 paragraph, it all would have been so much easier for me.
Posts: 4897  From: Cambridge, ON, Canada  Registered: Jun 2004
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ooby
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posted March 03, 2005 08:46
Bah! This isn't algebra. Know your maths.
 "haven't you ever wondered if there's more to life than being really, really, rediculously good looking?"
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Ivan
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posted March 05, 2005 18:51
Well, for one, in a right triangle, the hypotenus is always the larger side. So, a shorter leg over a longer leg will always fall between 0 and 1
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