Cosine Rule VARIANT (1 Viewer)

[Forbidden.]

The standard Cosine Rule to find an unknown angle with three included sides is as follows:

CosA = (b²+c²-a²) / (2bc)
CosB = (a²+c²-b²) / (2ac)
CosC = (a²+b²-c²) / (2ab)


A Cosine Rule variant, promoted by me and endorsed by friends have been proven to be much easier:

CosA = (a²-b²-c²) / (-2bc)
CosB = (b²-a²-c²) / (-2ac)
CosC = (c²-a²-b²) / (-2ab)



Try this problem, use both the original and the variant of the Cosine rule, you will come down to the same final answer:

Find an unknown angle in a triangle with the sides 3.8m, 5.6m and 7.1m in length.

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My personal thoughts on Mathematics Extension 1 and 2 Courses:
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To perform well in these two courses, there are two qualities which at least either must be posessed in order to meet specified criteria in the Maths course.


MOTIVATION:

Regardless of your mental capability or intelligence, if you are willing to learn and enjoy Maths, you will ultimately succeed in Maths due to your high morale.
Many students simply waste their time in junior Mathematics by simply talking, skipping homework and will not know what an obtuse angle is.
When they reach year 11, they will end up studying General Mathematics, as part of their continuation of lack of motivation, as General Mathematics is seen as a very "easy" course and requires little knowledge from previous years.


TALENT:

I overestimated myself when I decided to choose Mathematics Extension 1 for Year 11, let alone plans for Extension 2 for the HSC course.

Depending on how your brain works, most Mathematics Extension students are capable of remembering equations and graphs off by heart, such as 1/x², and if there are slight variations, such as 1/x²-5, they will not face any difficulties when asked to draw it on paper.

I as an Asian, I am assumed to remember ALL 17 theorems in Circle Geometry, which seems impossible to most Extension students in my class.
However, there are many students, especially from selective schools are capable of recalling all 17 theorems from Circle Geometry without difficulty.
There is a massive gap between me, my classmates and students from other schools excelling in Extension.

Chances are, there probably is a good chance of achieveing top marks in Extension 1 for students who are Mathematically talented, unofrunately I am not.

 

[SoulSearcher]

You can see in the variant cosA = (a²-b²-c²)/(-2bc) that if you multiply the RHS by -1/-1, it comes out to the same equation as the standard version, so unless there is a difficulty with the variant that I haven't seen yet, you can use it if you want to.

I wasted a lot of time in the junior years because I found the content particularly easy, it didn't offer me a challenge and thus I wouldn't put the effort in. That was why I accepted the challenge of accelerating maths in year 9, and haven't looked back. However, it is true that you should have the motivation to do and enjoy maths, and with a little bit of talent, you can indeed do very well in it.

I have a friend who, back in year 10 wanted to do extension 2 maths, but now shafted those plans because he found out that he wasn't doing well enough in 2 unit maths to be able to do well in extension 2 maths. Even though I'm an extension 1 maths student, I still find it difficult to remember the shapes of graphs like 1/x² off the top of my head, but then I've always hated graph-sketching

I didn't even know there were 17 theorems in circle geometry, although a few of them are converse theorems e.g. chords of equal length in equal circles are eqidistant from the centre, and chords in a circle which are equidistant from the centre are equal in length. But really, there should be no assumption that you should know everything about maths anyway just because you're an asian. It is all just a stereotype, and those stereotypes do not always live up to be true. Remember that hard work and effort usually beats pure talent alone, and you should not be worrying about the performance of other students from other schools for now, but rather focusing on your own work, and trying to improve youself in your weaker areas. I wish you good luck in your studies, and remember there is always people there to help you when you need it.

 

[Riviet]

The standard Cosine Rule to find an unknown angle with three included sides is as follows:

CosA = (b²+c²-a²) / (2bc)
CosB = (a²+c²-b²) / (2ac)
CosC = (a²+b²-c²) / (2ab)


A Cosine Rule variant, promoted by me and endorsed by friends have been proven to be much easier:

CosA = (a²-b²-c²) / (-2bc)
CosB = (b²-a²-c²) / (-2ac)
CosC = (c²-a²-b²) / (-2ab)

I would be very interested in seeing your proof of how your variation of the cosine rule is actually easier to use.

 

[acmilan]

 

[Forbidden.]

I would be very interested in seeing your proof of how your variation of the cosine rule is actually easier to use.

Despite being an Extension 1 student, I cannot show full proof, notice the cosine variant contains only minus signs in the numerator which makes it a tad easier to remember ... and hopefully the 2 Unit HSC markers will accept it ...

You can see in the variant cosA = (a²-b²-c²)/(-2bc) that if you multiply the RHS by -1/-1, it comes out to the same equation as the standard version, so unless there is a difficulty with the variant that I haven't seen yet, you can use it if you want to.

I wasted a lot of time in the junior years because I found the content particularly easy, it didn't offer me a challenge and thus I wouldn't put the effort in. That was why I accepted the challenge of accelerating maths in year 9, and haven't looked back. However, it is true that you should have the motivation to do and enjoy maths, and with a little bit of talent, you can indeed do very well in it.

I have a friend who, back in year 10 wanted to do extension 2 maths, but now shafted those plans because he found out that he wasn't doing well enough in 2 unit maths to be able to do well in extension 2 maths. Even though I'm an extension 1 maths student, I still find it difficult to remember the shapes of graphs like 1/x² off the top of my head, but then I've always hated graph-sketching

I didn't even know there were 17 theorems in circle geometry, although a few of them are converse theorems e.g. chords of equal length in equal circles are eqidistant from the centre, and chords in a circle which are equidistant from the centre are equal in length. But really, there should be no assumption that you should know everything about maths anyway just because you're an asian. It is all just a stereotype, and those stereotypes do not always live up to be true. Remember that hard work and effort usually beats pure talent alone, and you should not be worrying about the performance of other students from other schools for now, but rather focusing on your own work, and trying to improve youself in your weaker areas. I wish you good luck in your studies, and remember there is always people there to help you when you need it.

I made a big mistake studying Extension 1 Maths, the only benefit is my closest friends are in Extension 1.

Graph sketching is simply a waste of time if you dont remember off by heart, either the table of values will consume valuable time or the habit of plotting points on the x- and y-axis will.

There are at least several theorems in circle geometry, I will never achieve full marks in the 3 Unit Maths HSC if I was presented with a question on Circle Geometry, let alone gettting a few marks, maybe from only drawing the diagram with a dodgy proof ?

 

[till02]

gotta hate maths!!! to complicated

 

[SoulSearcher]

Despite being an Extension 1 student, I cannot show full proof, notice the cosine variant contains only minus signs in the numerator which makes it a tad easier to remember ... and hopefully the 2 Unit HSC markers will accept it ...

I really doubt that it is easier to use, but whatever you feel works for you, then go for it.

 

[volition]

What makes this any easier to use? I think somebody needs to spend less time jerking off.

 

[Forbidden.]

What makes this any easier to use? I think somebody needs to spend less time jerking off.

You do that don't you ?