Split - Answer with SD (Adding trigonometric waveforms...)

Cubist

Cubist

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The Highlander said:
Working to 2/3 d.p. throughout produces a final answer for the phase angle that is (usually) in keeping with what you get either way; since it needs to be declared to that kind of level of accuracy anyway in the end. ?
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Are you perchance an Engineer ? ? I took an Engineering degree - so I've done my fair share of giving answers to 2/3dp ;)

Either way (exact or 2/3dp) shows that the student knows how to use the techniques involved :thumbup: - but they should probably follow directions on the test paper (whatever they may be ?‍♂️)

The Highlander said:
Though I suspect Freckles has given up and gone elsewhere (perhaps to seek a 'ready-made' answer)! ?
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Possibly. They did respond a couple of times in this other thread, but they seem to have stopped posting before it reached a final answer.
 
Cubist said:
Are you perchance an Engineer ? ? I took an Engineering degree - so I've done my fair share of giving answers to 2/3dp ;)

Either way (exact or 2/3dp) shows that the student knows how to use the techniques involved :thumbup: - but they should probably follow directions on the test paper (whatever they may be ?‍♂️) Agreed, of course!
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Hi Cubist

After school I went to Glasgow Uni. (intent on studying Chemistry but out of forty graduates that year only two got jobs! ?) so I switched to Mechanical Engineering (and Marketing). So, if asked to 'pick a side', I probably would describe myself as an “Engineer”. (I certainly don’t consider myself a “Mathematician”!)

After graduation I spent twenty-odd years in the Engineering industries but, almost solely, in the Sales & Marketing side and so, forgot most of the Maths I’d ever learned!
I later went back to Glasgow to do an MBA but in the early nineties I decided to move into teaching and got myself a PGCE at Strathclyde qualifying me to teach Physics & Maths; I’ve taught in both subject areas but did spend more time in the Maths department. I’m effectively retired now (deservedly so having put up with cantankerous teenagers for nigh on three decades! ?), just working the odd day’s supply cover now and then.

When I went back into schools the curriculum had changed markedly from my schooldays (Synthetic Division was a term I’d never even heard of! ?) so I’ve had to re-learn much of my Mathematics myself (at the higher levels; including the Wave Function) and so my 'ability' level just doesn’t compare with the majority of the “tutors” in here (and so, I am very pleased to learn from their expertise); I suspect that the most I have to offer is, perhaps, an ability to explain some things in a way that addresses the needs of (some) new members that, possibly, the more advanced mathematicians in here take it for granted that everyone else finds as obvious as it is to them.

When I went to Glasgow, my first year subjects were Maths, Physics & Chemistry and I was surprised to learn that the Mathematics Department was located in the Faculty of Arts! However, if you accept the premise that Mathematics is a “language” with its own vocabulary, grammar & syntax, that then seems a perfectly sensible location for it. Accepting that ‘definition’ also goes a long way to explaining the kinds of ‘arguments’ that pop up in here from time to time too. For example, the OP in this thread clearly started it because a 'dispute' that he had with me (over percentage calculations) was removed by Subhotosh (for getting too “heated”?); I have to admit to being a little bit disappointed it was deleted because I firmly believe I won that argument! ?
I was going to add my own tuppence worth to that thread but I’m still waiting to hear what more Steven has to say when he finally finishes his sentence (“I am sorry but” ?) before I plough in. ?

In Scottish schools we punish (severely) any omission of units in the Physics departments! If the answer is 13 Amperes and a pupil gives me “13”, my usual response is “13 What? Bananas? That was what my (martinet) Physics teacher used to scream at us! ?
But in Maths we simply encourage (implore) pupils to remember to add the appropriate units at the end of their calculation(s) when appropriate. Most of the time we’re just happy if they get anywhere near the right answer (or even if their working looks like they’re heading in that direction! ?); there is no way that we would even consider penalising a pupil for writing ×100 (instead of ×100%) in their intermediate calculations (and might even award full marks if a final answer was written as 25 rather than 25%; depending on pupil ‘ability’).

On that percentages issue, after much consideration, my thinking is that, perhaps, the ×100 (with or without %) should be left out altogether!
An item sold at £1 goes up in price to £1.25.

The price increase is: \(\displaystyle \frac{£1.25-£1.00}{£1.00}=0.25\space=25\%\space=\frac{1}{4}\)

ie: the three equivalent (interchangeable?) fractions: a decimal fraction, a percentage fraction & a vulgar* fraction.​

The ×100 is implicit in the conversion between decimal & percentage fractions; a fact that the likes of us would have no problem with but, if you don’t specifically include it in the calculation(s) when dealing with youngsters (or less mathematically-minded adults) then chaos ensues and it won’t matter a jot to them whether the ×100 has a % sign after it or not!
As I’m sure you’re aware, the vast majority of the population just don’t care about these ‘niceties’, they too are only too happy if they can just get the right answer (by any means), it’s only folks like us who have time (& energy) enough to spare to ‘waste’ it on (passionate) arguments like these. Perhaps we spend too much time with our heads in the clouds but, then again, maybe that’s just our idea of fun? ?

*Showing my age there, aren’t I? I believe they are now referred to as “common fractions”, though I can’t say I’d be much happier to be described as “common” instead of “vulgar”! ?
 
Very interesting! It's great to know @The Highlander a little better!

The Highlander said:
When I went back into schools the curriculum had changed markedly from my schooldays (Synthetic Division was a term I’d never even heard of! ?) so I’ve had to re-learn much of my Mathematics myself (at the higher levels; including the Wave Function) and so my 'ability' level just doesn’t compare with the majority of the “tutors” in here (and so, I am very pleased to learn from their expertise); I suspect that the most I have to offer is, perhaps, an ability to explain some things in a way that addresses the needs of (some) new members that, possibly, the more advanced mathematicians in here take it for granted that everyone else finds as obvious as it is to them.
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It's probably good to have several replies in some threads, with different approaches and words, and then hopefully at least one of them will resonate with the student. Helping others is a great way to extend our own knowledge.

The Highlander said:
When I went to Glasgow, my first year subjects were Maths, Physics & Chemistry and I was surprised to learn that the Mathematics Department was located in the Faculty of Arts! However, if you accept the premise that Mathematics is a “language” with its own vocabulary, grammar & syntax, that then seems a perfectly sensible location for it. Accepting that ‘definition’ also goes a long way to explaining the kinds of ‘arguments’ that pop up in here from time to time too. For example, the OP in this thread clearly started it because a 'dispute' that he had with me (over percentage calculations) was removed by Subhotosh (for getting too “heated”?); I have to admit to being a little bit disappointed it was deleted because I firmly believe I won that argument! ?
I was going to add my own tuppence worth to that thread but I’m still waiting to hear what more Steven has to say when he finally finishes his sentence (“I am sorry but” ?) before I plough in. ?
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Maths certainly is a language. And fortunately algebraic notation actually seems reasonably global and agreed upon (unlike the spoken language, or even sign language which differs country to country). I think that due to the precise nature of mathematics and the observant and diligent nature of the people who are good at it, then when a disagreement happens it can indeed become a bit heated :LOL:

The Highlander said:
In Scottish schools we punish (severely) any omission of units in the Physics departments! If the answer is 13 Amperes and a pupil gives me “13”, my usual response is “13 What? Bananas? That was what my (martinet) Physics teacher used to scream at us! ?
But in Maths we simply encourage (implore) pupils to remember to add the appropriate units at the end of their calculation(s) when appropriate. Most of the time we’re just happy if they get anywhere near the right answer (or even if their working looks like they’re heading in that direction! ?); there is no way that we would even consider penalising a pupil for writing ×100 (instead of ×100%) in their intermediate calculations (and might even award full marks if a final answer was written as 25 rather than 25%; depending on pupil ‘ability’).
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My "A level" teacher was a stickler for laying out work in a neat/ readable way. This maximises the chance of picking up method marks. Also it's easier and faster to look back and double check your own work if you have spare time at the end of the exam (avoiding any "how the **** did I get that" moments)

In contrast, when my kids did their A-levels descriptive working wasn't necessary. I had trouble helping them if they became stuck due to the effort of working out what they were doing and where a particular equation appears from. How long does it take to write "Use cosine rule", etc

The Highlander said:
On that percentages issue, after much consideration, my thinking is that, perhaps, the ×100 (with or without %) should be left out altogether!
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That does make a lot of sense IMO. However, I'm very happy to go with the US convention myself while using this site. Judging by my own kids, the students involved will probably adopt the nomenclature they were taught when they write their own answers up anyway.

The Highlander said:
*Showing my age there, aren’t I? I believe they are now referred to as “common fractions”, though I can’t say I’d be much happier to be described as “common” instead of “vulgar”! ?
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Over the years my (dirty) mind has incorrectly merged "vulgar" and "improper" fractions! I had forgotten that they have different meanings :ROFLMAO:
 
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