double angle integration (1 Viewer)

[elliottjohnson]

Hi can somebody please explain how you get from finding the integral (S) of:

S (cos6x.cos2x) dx >> to 1/2 S (cos8x + cos4x) dx

not sure how to expand the double angle results that leave me with that as an answer??
thanks

 

[Trebla]

cos 8x + cos 4x
= cos (6x + 2x) + cos (6x - 2x)
= 2cos 6x cos 2x
=> cos 6x cos 2x = (cos 8x + cos 4x) / 2

 

[nat_doc]

would people recommed learning the results by heart?

 

[scardizzle]

yes..yes you should

 

[Aquawhite]

Just using that double angle theorum is rather fast and simply done on the side of the page as working... there would be no need to memorise it. That said, the double angle theorum isn't the first thing that comes to mind - but it's a very basic process.

 

[cutemouse]

yes..yes you should

Well if you have SKB then yes you should But generally in the HSC they ask you to prove it in a previous part if you need to use the result.

 

[random-1006]

its fairly basic.

for example, i would think it would be fairly reasonable to ask something like integrate sin(2x)cos(2x) dx in a 3 unit paper ( without the previous question like show 2sin(2x)cos(2x)= sin(4x) )

 

[nat_doc]

Well if you have SKB then yes you should But generally in the HSC they ask you to prove it in a previous part if you need to use the result.

what is SKB? and i bet a rep point that this year in the HSC, there will not be a "hint" question beforehand.... they will just give u the integral

who wants to bet?

 

[hscishard]

Me

 

[random-1006]

Me

they have given the hint before on an hsc, it was one of the 3 units before 2000

 

[random-1006]

Just using that double angle theorum is rather fast and simply done on the side of the page as working... there would be no need to memorise it. That said, the double angle theorum isn't the first thing that comes to mind - but it's a very basic process.

what is the first thing then?

 

[cutemouse]

what is SKB? and i bet a rep point that this year in the HSC, there will not be a "hint" question beforehand.... they will just give u the integral

who wants to bet?

SKB = teacher of scardizzle. I used to have him for the majority of Year 11/12. I'd say that he is one of the best teachers in the state.

BTW, this question could be done using integration by parts. You would get the original integral by 2 applications of IPB and then you could work out what the integral is that way. But this of course is a much longer method.

 

[Trebla]

I never memorise them. They're easy to derive on the spot when required.