Shannonscott96
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I do Alevel Maths on the EDEXCEL exam board. I have been taught CAST diagram so many times but can't get my head around them. Is there another way to solve these types of problems but with a different method?
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TenOfThem
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(Original post by Shannonscott96)
I do Alevel Maths on the EDEXCEL exam board. I have been taught CAST diagram so many times but can't get my head around them. Is there another way to solve these types of problems but with a different method?
Learn the rules or draw the graphs
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username1560589
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As tenofthem said, you can either learn each of the sine, cosine and tangent graphs separately or you can learn the general solutions for each function.
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Gaiaphage
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IMO it'll be much easier and better in the long run if you got help understanding the cast diagram than tried to find another method. There's a reason it's the default method! If you have any questions feel free to PM me/make a thread in the maths forum.
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Lolgarithms
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(Original post by Shannonscott96)
I do Alevel Maths on the EDEXCEL exam board. I have been taught CAST diagram so many times but can't get my head around them. Is there another way to solve these types of problems but with a different method?
What is it that you can't get your head around with the CAST diagram?
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TenOfThem
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(Original post by Gaiaphage)
IMO it'll be much easier and better in the long run if you got help understanding the cast diagram than tried to find another method. There's a reason it's the default method! If you have any questions feel free to PM me/make a thread in the maths forum.
It isn't the "default method"

TBH I think that the graphs are the standard method

I prefer CAST, personally, but I teach all 3 and encourage students to choose

CAST is the method that is most poorly taught, imo
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Gaiaphage
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(Original post by TenOfThem)
It isn't the "default method"
Why do you say that? It's the markscheme method, which I'd call synonymous to default method.
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Mr M
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(Original post by Shannonscott96)
I do Alevel Maths on the EDEXCEL exam board. I have been taught CAST diagram so many times but can't get my head around them. Is there another way to solve these types of problems but with a different method?
All you need to know is (in degrees):

\sin x = \sin (180 - x)

\sin x = \sin (x \pm 360)

\cos x = \cos (360 - x)

\cos x = \cos (x \pm 360)

\tan x = \tan (x \pm 180)

I have never bothered with the CAST diagram and have never taught anyone who has found it difficult to master and apply these rules.
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TenOfThem
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(Original post by Gaiaphage)
Why do you say that? It's the markscheme method, which I'd call synonymous to default method.
What "markscheme"
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tiny hobbit
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(Original post by Gaiaphage)
Why do you say that? It's the markscheme method, which I'd call synonymous to default method.
Which mark schemes are you looking at? I've just been looking at some Edexcel C2 schemes for various years. They all just go straight in, i.e. effectively the "learn the different formulae" version.
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Gaiaphage
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(Original post by tiny hobbit)
Which mark schemes are you looking at? I've just been looking at some Edexcel C2 schemes for various years. They all just go straight in, i.e. effectively the "learn the different formulae" version.
Fair enough Edexcel might not - I hadn't looked at them. The only ones I bother doing are Solomons which cover every exam board and they use the cast diagram so I'd assumed that every board did, maybe it's just too complicated for the standard student.
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username1560589
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(Original post by Gaiaphage)
Fair enough Edexcel might not - I hadn't looked at them. The only ones I bother doing are Solomons which cover every exam board and they use the cast diagram so I'd assumed that every board did, maybe it's just too complicated for the standard student.
You should do your board's ones as well to get used to their specific question and mark scheme style.
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TenOfThem
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(Original post by Gaiaphage)
Fair enough Edexcel might not - I hadn't looked at them. The only ones I bother doing are Solomons which cover every exam board and they use the cast diagram so I'd assumed that every board did, maybe it's just too complicated for the standard student.
Solomon papers are unofficial. They do not represent any boards.

No board , to my knowledge, species a method for this - I would be surprised if they did since any of the 3 methods referred to in this thread are equally valid.


BTW I have just looked at some C3 mark schemes for Solomon papers and they show NO method
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tiny hobbit
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(Original post by Gaiaphage)
Fair enough Edexcel might not - I hadn't looked at them. The only ones I bother doing are Solomons which cover every exam board and they use the cast diagram so I'd assumed that every board did, maybe it's just too complicated for the standard student.
If the Solomon papers did use a CAST diagram (which they don't), that would tell you the views of one teacher (Shaun Armstrong) on which method is best.

I have to say (yet again) that it's really cheeky for physicsandmathstutor to put PhysicsAndMathsTutor.com on the top of papers written (and sold to make a living) by someone else.
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TeeEm
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I have never ever taught anything else but a fully algebraic method using standard results producing a general solution.
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TenOfThem
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(Original post by TeeEm)
I have never ever taught anything else but a fully algebraic method using standard results producing a general solution.
Do you mean that you just teach the rules (shown by Mr M)?
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TeeEm
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(Original post by TenOfThem)
Do you mean that you just teach the rules (shown by Mr M)?
absolutely! I have never used anything else.

I set it a bit different, (as a pair of equations)
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Sir Cumference
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I teach using different methods but I wonder if fewer students would be confused by trig if the CAST diagram became less popular and trig graphs became more popular?

As TenOfThem said, CAST is poorly taught (not by me of course!). And I find that often students who only do trig using the CAST diagram are less familiar with the trig graphs which can be a disadvantage.

It seems as though the diagram is useful, mainly because students don't know the trig graphs well enough to be able to learn the rules (given by MrM) for non-acute angles.
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TenOfThem
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(Original post by notnek)
As TenOfThem said, CAST is poorly taught (not by me of course!). And I find that often students who only do trig using the CAST diagram are less familiar with the trig graphs which can be a disadvantage.
You see - I think this is the issue

I teach CAST as a visual reminder of the graphs (I use an excellent tool that draws the graphs as you move around the circle) but I teach the symmetry of both and my initial CAST diagram has the formulae on

I teach all the methods because different students prefer different methods

IMO the choice is to
  • Learn a load of rules
  • Learn 3 graphs
  • Understand one visualistation technique


I certainly teach students who do not visualise in the same way I do - teaching them just CAST would be foolish but I have known plenty for whom the learning of rules feels pointless (I would be one of them)
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