Products as sums or differences (1 Viewer)

[812]

I'm having difficulties doing products as sums or differences questions.

I can eventually do them, but each question takes ages to do because it takes a long time to derive the formulas from the double angle formulas in my head.

So for all you people good at trig, what's the best way to approach these questions? Do you use logic and derive the formulas in your head or do you just memorize the formulas and basically plug the question into the formula?

e.g. Express the following as sums or differences: 2sin(4x)cos(2x)

 

[jnney]

how many of those questions have you done?

 

[SpiralFlex]

I'm having difficulties doing products as sums or differences questions.

I can eventually do them, but each question takes ages to do because it takes a long time to derive the formulas from the double angle formulas in my head.

So for all you people good at trig, what's the best way to approach these questions? Do you use logic and derive the formulas in your head or do you just memorize the formulas and basically plug the question into the formula?

e.g. Express the following as sums or differences: 2sin(4x)cos(2x)

Here's a trick to remember them.

First of all I will list the formulae out.









Now let's inspect these formulae.

We know we have a combination of messy expansions. But what can we see that is similar? Looking closely I can see that the terms on the RHS will always be first [The average of the sums of A and B] then [The average of the differences of A and B]

Now all we need to do is to memorise the trigonometric identity.

In short,


[S+S]=2[SC]
[S-S]=2[CS]

[C+C]=2[CC]
[C-C]=-2[SS]

Note: The cosines are the ones with the same identities together. In other words you can think of "same sex marriage".


Now, let us go backwards!









On first examination,

We see on RHS again! We have the same terms. You have your trigonometric function then, A+B and A-B.

So they stay the same.

Now,

2[SC]=[S+S]

2[CS]=[S-S]

2[CC]=[C+C]

-2[SS]=[C-C]

Now there is a pattern with going back and forth, but I will let you figure that out for yourself. Connect the dots.

 

[Carrotsticks]

Products as sums or differences was removed from the syllabus a while ago. It is no longer really taught at school. I highly doubt it will appear in the HSC (unless they first ask you to derive it).

However, it can still be examined (since the derivation of them can be done using techniques within the syllabus).

It's a useful tool sometimes, especially for Integration.

 

[SpiralFlex]

Products as sums or differences was removed from the syllabus a while ago. It is no longer really taught at school. I highly doubt it will appear in the HSC (unless they first ask you to derive it).

However, it can still be examined (since the derivation of them can be done using techniques within the syllabus).

It's a useful tool sometimes, especially for Integration.

Some schools will still teach it.

My recommendation to the OP is to learn it if your school has taught it as the school can basically put anything you have learnt in the trials and your assessments.

 

[Carrotsticks]

Some schools will still teach it.

My recommendation to the OP is to learn it if your school has taught it as the school can basically put anything you have learnt in the trials and your assessments.

I'm guessing that his school has taught it, otherwise why would he be asking questions about it on BOS.

The Coroneos and Cambridge Year 11 textbook have a plethora of these questions.

 

[SpiralFlex]

I'm guessing that his school has taught it, otherwise why would he be asking questions about it on BOS.

The Coroneos and Cambridge Year 11 textbook have a plethora of these questions.

Only the Year 12 book.

 

[Carrotsticks]

Only the Year 12 book.

My bad, the green one.

Nobody gives Coroneos any credit =(

 

[SpiralFlex]

My bad, the green one.

Nobody gives Coroneos any credit =(

I do. The detail in such a small book for 4U is extraordinary.

I also liked the 3U book. Orange colour is fun to look at.

 

[Carrotsticks]

I do. The detail in such a small book for 4U is extraordinary.

I also liked the 3U book. Orange colour is fun to look at.

Have you seen the Supplementary 4U Coroneos?

It has such nice Mechanics diagrams.

Seriously, if somebody bothered typing out the entire Coroneos series (with computer-drawn diagrams), it would be the best textbook in the market for the next few generations.

In fact, when I first bought the fat brown Coroneos Extension 1 book a couple of months ago, my mum walked past, saw it, then commented "Oh! I remember using that textbook when I was in high school".

 

[SpiralFlex]

Have you seen the Supplementary 4U Coroneos?

It has such nice Mechanics diagrams.

Seriously, if somebody bothered typing out the entire Coroneos series (with computer-drawn diagrams), it would be the best textbook in the market for the next few generations.

In fact, when I first bought the fat brown Coroneos Extension 1 book a couple of months ago, my mum walked past, saw it, then commented "Oh! I remember using that textbook when I was in high school".

Yeah my former 3U teacher used it too. She is 45+

I have seen the supplementary but don't own it as of yet. I need to save up though.

The font is not bad to people who like maths, they should appreciate it regardless of the form. I quite like the font, appreciate the days of 1980s maths. I had never experienced before.

My friend got free Coroneos books as he got them from his tutoring centre in which the coordinator knew the Coroneos long ago.

 

[812]

Thanks guys.

Yeah my school has taught it.

There was also a question on it in my 3u first assessment, and I couldn't do it in the exam

It seems like I forget everything very quickly if I don't touch it for a while. Not enough practice I guess...

I'm currently doing chapter 21 in the green Fitzpatrick book.

For some reason, I'm finding X1 harder than X2 so far.

 

[SpiralFlex]

Thanks guys.

Yeah my school has taught it.

There was also a question on it in my 3u first assessment, and I couldn't do it in the exam

It seems like I forget everything very quickly if I don't touch it for a while. Not enough practice I guess...

I'm currently doing chapter 21 in the green Fitzpatrick book.

For some reason, I'm finding X1 harder than X2 so far.

Which question was that? On products? This is why I think its best to revise what you have learnt in school even though its not part of the syllabus + the syllabus.

 

[Carrotsticks]

For some reason, I'm finding X1 harder than X2 so far.

Most likely because MX1 is so much more content-heavy than MX2, and this spells disaster for the forgetful student.

 

[812]

Which question was that? On products? This is why I think its best to revise what you have learnt in school even though its not part of the syllabus + the syllabus.

Yeah on products. They asked to derive the formula first and then solve it.

Most likely because MX1 is so much more content-heavy than MX2, and this spells disaster for the forgetful student.

I came top 10 for my 4u assessment but only average for my 3u assessment. An absolute disaster indeed.

My teacher teaches very fast in class and sometimes I don't end up doing all the homework. i.e. what I learn in class is not consolidated properly and quickly forgotten.

 

[SpiralFlex]

Yeah on products. They asked to derive the formula first and then solve it.



I came top 10 for my 4u assessment but only average for my 3u assessment. An absolute disaster indeed.

My teacher teaches very fast in class and sometimes I don't end up doing all the homework. i.e. what I learn in class is not consolidated properly and quickly forgotten.

Ask questions! If not your teacher at least here then!

Consolidate! Do your homework!

Past HSC papers!

 

[Carrotsticks]

Yeah on products. They asked to derive the formula first and then solve it.

How did they ask you to derive it? Was it a 'here's the formula, prove it', or was it a 'prove the product formula' (without actually giving it to you)?

If the first, that should be okay. Just a few applications of compound angle formulae, no need for memorising.

If the latter.... that's just bad luck.

My teacher teaches very fast in class and sometimes I don't end up doing all the homework. i.e. what I learn in class is not consolidated properly and quickly forgotten.

You could always hire tutor here to help solidify the knowledge first planted in from your teacher.

Not to have regularly (Unless you want to), but perhaps after each topic, have a few hours with a tutor to confirm everything.

Alternatively, you can post questions here.

 

[812]

How did they ask you to derive it? Was it a 'here's the formula, prove it', or was it a 'prove the product formula' (without actually giving it to you)?

If the first, that should be okay. Just a few applications of compound angle formulae, no need for memorising.

If the latter.... that's just bad luck.



You could always hire tutor here to help solidify the knowledge first planted in from your teacher.

Not to have regularly (Unless you want to), but perhaps after each topic, have a few hours with a tutor to confirm everything.

Alternatively, you can post questions here.

Yeah they gave me the formula and asked me to prove it. I proved like half of it and then just wrote = RHS

But for some reason, the marker gave me full marks for it even though I didn't fully prove it. (Probably lazy marker LOL)

I didn't get any marks for the next part though.

 

[Carrotsticks]

Yeah they gave me the formula and asked me to prove it. I proved like half of it and then just wrote = RHS

But for some reason, the marker gave me full marks for it even though I didn't fully prove it. (Probably lazy marker LOL)

I didn't get any marks for the next part though.

Haha nice work on your successful fudging. Many markers are lazy like that.

 

[Kimyia]

Yeah they gave me the formula and asked me to prove it. I proved like half of it and then just wrote = RHS

But for some reason, the marker gave me full marks for it even though I didn't fully prove it. (Probably lazy marker LOL)

I didn't get any marks for the next part though.

Lol, I fudged my working in a practice topic test I was doing once for 2U and I got the mark for it
But I reading this thread I was freaking out because I've never heard of the product as sums or differences let alone done it in class. My question now is, could they ever ask a question on this in the HSC and if so, is it best I learn it? My textbook is maths in focus so I don't think it has it in there.