ApeNz

14-10-2004, 09:57 PM

HI , I was wondering if anyone knew how the cosine rule is Derived , the rule is a2 = b2 + c2 - 2 xbc * cos (angle) - the twos at the front are meant to be to the power of twos. Thanks

Ape

Ape

View Full Version : [ OT ] Cosine Rule

ApeNz

14-10-2004, 09:57 PM

HI , I was wondering if anyone knew how the cosine rule is Derived , the rule is a2 = b2 + c2 - 2 xbc * cos (angle) - the twos at the front are meant to be to the power of twos. Thanks

Ape

Ape

ApeNz

14-10-2004, 09:59 PM

rule is a2 ( power of two ) = b2 ( power of two ) + c2 ( power of two ) - 2 * bc cos ( angle )

~~~~~ s y ~~~~~

14-10-2004, 10:12 PM

Do you REALLY have to get my brain going? :(

c2 = a2 + b2 - a·sin(B)·b·sin(A) - a·sin(B)·b·sin(A) + 2ab·cos(A)·cos(B)

= a2 + b2 + 2ab(cos(A)cos(B) - sin(A)sin(B))

= a2 + b2 + 2ab(cos(A + B))

= a2 + b2 + 2ab(cos(180o - C))

= a2 + b2 - 2ab(cos(C))

As you would know, they 2's after the a and b's are squares, while the other ones are multiples. If you get stuck, get back and ask. Google does produce much decent answers for this though. Hope you haven't forgotten it :D

c2 = a2 + b2 - a·sin(B)·b·sin(A) - a·sin(B)·b·sin(A) + 2ab·cos(A)·cos(B)

= a2 + b2 + 2ab(cos(A)cos(B) - sin(A)sin(B))

= a2 + b2 + 2ab(cos(A + B))

= a2 + b2 + 2ab(cos(180o - C))

= a2 + b2 - 2ab(cos(C))

As you would know, they 2's after the a and b's are squares, while the other ones are multiples. If you get stuck, get back and ask. Google does produce much decent answers for this though. Hope you haven't forgotten it :D

R2x1

14-10-2004, 10:14 PM

Written as a^2 = b^2 + etc.

It's derived from page 73 in my old book ;)

It's derived from page 73 in my old book ;)

alphazulusixeightniner

15-10-2004, 12:44 AM

I think they give you one equation in the exam (is that right?) and then you can easily re-arrange them to suit yourself for working out the question.

ApeNz

15-10-2004, 08:25 AM

Thanks , yeah they do give it in the exam , i just wanted to know how they got it - helps me understand things more

Prescott

15-10-2004, 04:44 PM

what maths are you doing? year 11 or year 12??

last year in maths (year 11) there was a trig paper but it never had the cosine rule. actually we did the cosine this year in maths but it was a internal. im 99.9999999% sure that this isnt in the exams

last year in maths (year 11) there was a trig paper but it never had the cosine rule. actually we did the cosine this year in maths but it was a internal. im 99.9999999% sure that this isnt in the exams

Jams

15-10-2004, 05:28 PM

hehehe, Soh Cah Toa.

DangerousDave

15-10-2004, 06:55 PM

I hate trig, wait a second, i hate maths slash school altogether!

- David

- David

Prescott

15-10-2004, 07:17 PM

trig isnt that bad, its not that hard either

george12

15-10-2004, 09:01 PM

Hehe, I finished my Trig last term :) (Level 1).

Got Merit i *think*.

George

Got Merit i *think*.

George

ApeNz

15-10-2004, 09:09 PM

im year 11 , i have been looking over some practice papers and the cosine and sine rules are there yet they change the content of the exams each year

ApeNz

15-10-2004, 09:10 PM

hey george - isnt trig a external you might have a practice - the cosine and sine rules are normal execellence questions

~~~~~ s y ~~~~~

15-10-2004, 09:30 PM

NO WAY that those things will come up in Level One... small chances in level two. ... small....

ApeNz

15-10-2004, 09:48 PM

My teacher says they might and thats enough for me to study for it - and we are learning about it so why won't it ?

george12

15-10-2004, 09:52 PM

Yeah, it was a 'mock' exam at the end of Term 3, to prepare us for the end of year externals. It didn't include the Sine or Cosine rules, neither does the real thing.

But there was a 'Sine and Cosine rule suppliment' made by my school.

I'm actually in Year 10, but there's an 'accelerate' class that does NCEA Level 1 for Maths and Science (Wellington College).

But I have finished learning it in class, done the mock test for it (the suppliment thing wasn't NCEA it was just out of 15), I got 12 out of 15 as far as I remember.

Cheers

But there was a 'Sine and Cosine rule suppliment' made by my school.

I'm actually in Year 10, but there's an 'accelerate' class that does NCEA Level 1 for Maths and Science (Wellington College).

But I have finished learning it in class, done the mock test for it (the suppliment thing wasn't NCEA it was just out of 15), I got 12 out of 15 as far as I remember.

Cheers

Jaguar

15-10-2004, 09:54 PM

What about those of us doing Cambridge exams?! :P

Easy way to remember it, you'll notice the first bit closely resembles Pythagoras' Theorem... a^2 = b^2 + c^2

So just remember -2bc cos A

Easy way to remember it, you'll notice the first bit closely resembles Pythagoras' Theorem... a^2 = b^2 + c^2

So just remember -2bc cos A

ApeNz

15-10-2004, 09:56 PM

Remember im only fifth form - isnt cambridge 6th ? thats how it is at my school

ApeNz

15-10-2004, 10:00 PM

I actally accepted my invitation into cambrige maths but now im thinking all you do is sit extra exams !! , no extra credits , But anyway I have a strong sense that Those rules will be in the exams they are not hard - yet i cant tell you until 11/11/04

ApeNz

15-10-2004, 10:02 PM

or do you mean Cambridge high school - im confused. Thinks . . .. . . . Fails

Jaguar

15-10-2004, 10:03 PM

I mean the IGCSE exams. I'm fourth form and doing IGCSE Maths, Combined Science and a couple of English papers. Next year AS and Form 7 A2. Tense stuff.

ApeNz

15-10-2004, 10:05 PM

We dont have that sort of stuff at our school - you do fourth form in fourth form and so on

Jaguar

15-10-2004, 10:09 PM

Believe me, you're not missing out on anything.

ApeNz

15-10-2004, 10:11 PM

a little challenge is always good

~~~~~ s y ~~~~~

15-10-2004, 10:34 PM

I've been through all this, I will come back tomorrow with a nice little explanation detail for anyone confused about NCEA, Cambridge, etc.

ApeNz

15-10-2004, 10:36 PM

all i know is that NCEA sucks and cambridge is a city with a high school that cheats - any more - well you tell me

~~~~~ s y ~~~~~

15-10-2004, 10:38 PM

No, Cambridge as in the proper system.

Cambridge International Examinations, set by the Cambridge University in England. World class qualification, Jaguar can explain the start, I'll sum it up when I get back ;-)

Cambridge International Examinations, set by the Cambridge University in England. World class qualification, Jaguar can explain the start, I'll sum it up when I get back ;-)

ApeNz

15-10-2004, 10:40 PM

i know that - i have been invited into the system myself

Growly

16-10-2004, 12:07 AM

Please don't get me started on NCEA.

It's stupid.

Latest example; you get the highest percentage in the class, the required amount of merit questions correct, the requires amount of achievement questions correct, and the required amount of excellence questions correct.

You don't get the right excellence questions correct. What do you get? Merit. What do the schmuks who managed to get fewer right get? Excellence.

Comes back to the hole 50% Excellence, 99% and Fail scenario.

Although in maths biggest question is interpreting questions, the math is easy. Take for example the question:

"John is building two square decks. He has enough decking to cover 34 square metres. He wants one deck to be longer by 2 metres.

Find the dimensions of each deck."

Now in my panicked state during the exam, I read this to mean that the decks, although orginally intended to be square, are now a square and a rectangle. Meaning that the algebraic equation to solve it would be, if you let x = the size of the width of the smaller deck, x^2 + x(x+2) = 34, which solves to be x = ~3.65 and the longer length about ~5.65. Unfortunately my English interpretation fails me , and be it absence of mind or what not, turns out that the second deck was also square, but each side was longer by 2m, not only one, as the "2 metres longer" suggests.

Therefore the answer would infact be x^2 + (x+2)^2 = 34, which solves to be x = 3 and the longer sides = 5.

That sucks. I can't believe such trivial confusions in language can get me. But, just as a matter of interest, how many people actually interpreted it to mean that the second square was infact 2 metres longer both ways? Now ofcourse most of you will, because I have blatantly pointed it out... but nevertheless?

It's stupid.

Latest example; you get the highest percentage in the class, the required amount of merit questions correct, the requires amount of achievement questions correct, and the required amount of excellence questions correct.

You don't get the right excellence questions correct. What do you get? Merit. What do the schmuks who managed to get fewer right get? Excellence.

Comes back to the hole 50% Excellence, 99% and Fail scenario.

Although in maths biggest question is interpreting questions, the math is easy. Take for example the question:

"John is building two square decks. He has enough decking to cover 34 square metres. He wants one deck to be longer by 2 metres.

Find the dimensions of each deck."

Now in my panicked state during the exam, I read this to mean that the decks, although orginally intended to be square, are now a square and a rectangle. Meaning that the algebraic equation to solve it would be, if you let x = the size of the width of the smaller deck, x^2 + x(x+2) = 34, which solves to be x = ~3.65 and the longer length about ~5.65. Unfortunately my English interpretation fails me , and be it absence of mind or what not, turns out that the second deck was also square, but each side was longer by 2m, not only one, as the "2 metres longer" suggests.

Therefore the answer would infact be x^2 + (x+2)^2 = 34, which solves to be x = 3 and the longer sides = 5.

That sucks. I can't believe such trivial confusions in language can get me. But, just as a matter of interest, how many people actually interpreted it to mean that the second square was infact 2 metres longer both ways? Now ofcourse most of you will, because I have blatantly pointed it out... but nevertheless?

Growly

16-10-2004, 12:10 AM

*Edit : interpreting questions is my biggest problem, not my biggest question. Apologies, it's late.

Oh, and at our school you are in no way allowed to sit levels higher than you otherwise the hole school does it. Grrrrr.

Oh, and at our school you are in no way allowed to sit levels higher than you otherwise the hole school does it. Grrrrr.

george12

16-10-2004, 12:16 AM

I remember doing that question. So we are both doing Level 1.

Yes, NCEA is strange I agree. What ever was wrong with the way things were in Year 9 - 92% or whatever instead of "Merit" - what the s*t does that tell you (until you go thru the test)

George

Yes, NCEA is strange I agree. What ever was wrong with the way things were in Year 9 - 92% or whatever instead of "Merit" - what the s*t does that tell you (until you go thru the test)

George

Greg S

16-10-2004, 12:49 AM

> trig isnt that bad, its not that hard either

Yeah, trig and geometry are the coolest! :)

Yeah, trig and geometry are the coolest! :)

george12

16-10-2004, 12:54 AM

There's a lot more young people here (me included) than I would have guessed. Who here is under 16? (just out of curiosity)

*puts hand up*

*puts hand up*

Greg S

16-10-2004, 01:13 AM

> There's a lot more young people here (me included)

> than I would have guessed. Who here is under 16?

16??? Sheesh two of my children are older than 16!

> than I would have guessed. Who here is under 16?

16??? Sheesh two of my children are older than 16!

lagbort

16-10-2004, 07:55 AM

growly, yes we are, robby and I are both doing level 2 classics this year remember, plus the various level 2 maths internals during the year

Jaguar

16-10-2004, 08:28 AM

I hope you feel very old... :P

I'm under 16 George.

For those curious on CIE (Cambridge International Examinations):

It's an international qualification and is quite reputable. There are three general levels of it, the IGCSE level, the AS level and A2 level. Usually IGCSE is done in fifth form (I'm doing it one year earlier) and from what I gather, many universities require some numerical qualification... a D grade of better in IGCSE does suffice.

AS and A2, once you've done both, combine to form an 'A level' qualification. I'm sure many of you would have heard of it. What I enjoy about Cambridge which is better than the NCEA system is that there's none of that Achieved, Merit, Excellence rubbish. You just get the good ol' percent and that counts towards a grade. :)

From what I gather, CIE still seems to be in its infancy in NZ as far as being widely used. If you want more info, head to the CIE Online Site (http://www.cie.org.uk). Have a browse through some of the syllabus of some subjects and compare to NCEA. You'll see that it's a lot more involved.

I'm under 16 George.

For those curious on CIE (Cambridge International Examinations):

It's an international qualification and is quite reputable. There are three general levels of it, the IGCSE level, the AS level and A2 level. Usually IGCSE is done in fifth form (I'm doing it one year earlier) and from what I gather, many universities require some numerical qualification... a D grade of better in IGCSE does suffice.

AS and A2, once you've done both, combine to form an 'A level' qualification. I'm sure many of you would have heard of it. What I enjoy about Cambridge which is better than the NCEA system is that there's none of that Achieved, Merit, Excellence rubbish. You just get the good ol' percent and that counts towards a grade. :)

From what I gather, CIE still seems to be in its infancy in NZ as far as being widely used. If you want more info, head to the CIE Online Site (http://www.cie.org.uk). Have a browse through some of the syllabus of some subjects and compare to NCEA. You'll see that it's a lot more involved.

Tom McB

16-10-2004, 09:10 AM

G,

The IT landscape is chockfull of debris from doomed (and need I mention horribly expensive) projects many of which can be attributed (but not limited) to a failure to grasp the fundamental questions.

There is a whole industry of toolsets aimed at reducing confusion brought about by vagaries of language and users who say one thing yet mean another.

T

The IT landscape is chockfull of debris from doomed (and need I mention horribly expensive) projects many of which can be attributed (but not limited) to a failure to grasp the fundamental questions.

There is a whole industry of toolsets aimed at reducing confusion brought about by vagaries of language and users who say one thing yet mean another.

T

basil

16-10-2004, 09:47 AM

Has all this got anything to do with the Native American Indian Rule?

That rule was made up by an Indian who had three wives and, when they slept in their teepee on animal skins, one of them was as good the other two put together. So he reckoned that "the squaw on the hippoptamus hide was equal to the sum of the squaws on the other two hides".

That rule was made up by an Indian who had three wives and, when they slept in their teepee on animal skins, one of them was as good the other two put together. So he reckoned that "the squaw on the hippoptamus hide was equal to the sum of the squaws on the other two hides".

Prescott

16-10-2004, 01:09 PM

> There's a lot more young people here (me included)

> than I would have guessed. Who here is under 16?

> (just out of curiosity)

>

> *puts hand up*

yea im 16 (turned 16 in aug) and im in year 12 (level 2)

> than I would have guessed. Who here is under 16?

> (just out of curiosity)

>

> *puts hand up*

yea im 16 (turned 16 in aug) and im in year 12 (level 2)

ApeNz

16-10-2004, 08:16 PM

im 15 but at my school they dont put you up even if you know more then the teacher so im stuck in year 11 for a few weeks anyway

ApeNz

16-10-2004, 08:20 PM

maths isn't that bad compared to IP - i do programming and we did like 2 weeks of programming and then 2 weeks of web design and the REST IS WRITTEN WORK , key factores , brief , you name it we write it , its just crap , Computing is about computers not writing about how you are going to do something and who its going to affect

ApeNz

16-10-2004, 08:21 PM

IT not IP

Growly

16-10-2004, 08:46 PM

>growly, yes we are, robby and I are both doing level 2 classics this year remember, plus the various level 2 maths internals during the year

You misunderstand...

Our school does not allow, for examples, Year 11s to do Year 12 maths. We do however, as I already said ("otherwise the [w]hole school does it"), do higher level assessments if they are across the year level. Therefore no one special person does a higher level, unless everyone else can too.

The subjects which no one likes, not many take, or are hard to administer due to lack of staff, are open to many year levels. For example, as in lagbort's Classics class, there are a whole 6 people, made up of year 11 and 12 students. Another example is that no one takes Year 11 IT, they all take Year 12 or 13 even if they are in Year 11 or not.

Which is kinda sad when you hear people going on about how young they are and what high levels they are doing, because, as much with NCEA, it simply isn't fair across the board.

Another example of this is an assessment our class did - I managed to miss out on an Excellence (I'm getting sick of this) because i used, in my rush, the word "select a sample" instead of "take a sample". Now if you think hard enough you'll understand the difference, but the key point here is that this was labelled as a "misconception", and, as it was an internal assessment, allowed the in-school markers to give me merit, not excellence. Everything else was right. The thing that got me was that another school did not have such criteria in their marking - which proves to me that nothing is fair!

Whether NCEA is aimed to prove to youngins that life is not fair at a very early stage or not, I'm moving to another country.

I avidly dislike NCEA!

You misunderstand...

Our school does not allow, for examples, Year 11s to do Year 12 maths. We do however, as I already said ("otherwise the [w]hole school does it"), do higher level assessments if they are across the year level. Therefore no one special person does a higher level, unless everyone else can too.

The subjects which no one likes, not many take, or are hard to administer due to lack of staff, are open to many year levels. For example, as in lagbort's Classics class, there are a whole 6 people, made up of year 11 and 12 students. Another example is that no one takes Year 11 IT, they all take Year 12 or 13 even if they are in Year 11 or not.

Which is kinda sad when you hear people going on about how young they are and what high levels they are doing, because, as much with NCEA, it simply isn't fair across the board.

Another example of this is an assessment our class did - I managed to miss out on an Excellence (I'm getting sick of this) because i used, in my rush, the word "select a sample" instead of "take a sample". Now if you think hard enough you'll understand the difference, but the key point here is that this was labelled as a "misconception", and, as it was an internal assessment, allowed the in-school markers to give me merit, not excellence. Everything else was right. The thing that got me was that another school did not have such criteria in their marking - which proves to me that nothing is fair!

Whether NCEA is aimed to prove to youngins that life is not fair at a very early stage or not, I'm moving to another country.

I avidly dislike NCEA!

Growly

16-10-2004, 08:51 PM

> maths isn't that bad compared to IP - i do programming and we did like 2 weeks of programming and then 2 weeks of web design and the REST IS WRITTEN WORK , key factores , brief , you name it we write it , its just crap , Computing is about computers not writing about how you are going to do something and who its going to affect

Yeah, I completely agree - I got so bored I decided to go to poly and do levels 5 & 6, after which I sat Network+. Then I came back to school and had to do level 3 during the day - which was crap.

BUT LUCKILY FOR ALL OF US THERE'S NO NCEA CRAP!

Yeah, I completely agree - I got so bored I decided to go to poly and do levels 5 & 6, after which I sat Network+. Then I came back to school and had to do level 3 during the day - which was crap.

BUT LUCKILY FOR ALL OF US THERE'S NO NCEA CRAP!

miknz

16-10-2004, 09:57 PM

I noticed in the early posts to this thread that Jams refered to Soh Cah Toa. This triggered a very frightening flash back to the old school days but I just cant remember what the hell it means/stands for. Someone care to refresh my memory?

miknz

16-10-2004, 10:08 PM

Or maybe the reason I cant remember what Soh Cah Toa is is because I was too busy learning to smoke, chatting up girls and driving the old Corolla up and down gravel roads during my 5th and 6th form maths periods. LOL. Suppose there is a mathmatical equation for a 1350kg car power sliding around a back country road, wonder if Soh Cah Toa applies?

~~~~~ s y ~~~~~

16-10-2004, 10:10 PM

sine = opposite / hypertenuse

cosine = adjacent / hypertenuse

tangent = opposite / adjacent

cosine = adjacent / hypertenuse

tangent = opposite / adjacent

Growly

16-10-2004, 10:11 PM

Sin = Opposite / Hypotenuse; Cosine = Adjacent / Hypotenuse; Tangent = Opposite / Adjacent

Soh Cah Toa!

Soh Cah Toa!

Growly

16-10-2004, 10:11 PM

I hate being late.

miknz

16-10-2004, 10:14 PM

click

Eric Richards

17-10-2004, 08:40 AM

you mean like this, not all that hard to do.

HI , I was wondering if anyone knew how the cosine

rule is Derived , the rule is a² = b² + c² - 2bc *cos (angle)

- the twos at the front are meant to be

to the power of twos. Thanks

Ape

HI , I was wondering if anyone knew how the cosine

rule is Derived , the rule is a² = b² + c² - 2bc *cos (angle)

- the twos at the front are meant to be

to the power of twos. Thanks

Ape

ApeNz

17-10-2004, 11:12 AM

Thanks for that. Ncea has made things alot crapper then before at least then if you crapped around the whole year and then studied for your exams you would be ok - now with all the internals and this and that you have to be good all year - not to say that im not

Powered by vBulletin® Version 4.2.5 Copyright © 2019 vBulletin Solutions Inc. All rights reserved.