P4 Maths Problem

[mortiz]

hi, I was wondering if someone could explain to me the following:

I'm doing a past P4 Maths Paper (AQA January 2003) and i've come a cropper on a specific question.

The question asks you to show (3sin2x + cos2x)^2 in the form Asin4x + Bcos4x + C. I've multiplied out the brackets to get 9(sin2x)^2 + (cos2x)^2 + 6sin2xcos2x and replaced 6sin2xcos2x with 3sin4x. The problem was wondering where to go next, after much pondering I decided to look at the Mark Scheme and I saw the following replacements: 9(sin2x)^2 = (9/2)(1-cos4x) and (cos2x)^2 = (1/2)(1 + cos4x) . Needless to say these baffled me even more.

Does someone mind explaining how they got from the left equations in both cases to the right one? It says something about the double angle formulae but I don't see how using that would help get the above replacements.

 

[KagePrototype]

I'm rather glad I didn't do Maths for A-level....

 

[marksmanHL2 :)]

Thats further maths surely.... (Me barfs!)

 

[Lil' Timmy]

sounds like you are already there mortiz:

you have 9(sin2x)^2 + (cos2x)^2 + 3sin4x

as you correctly noticed, the indenties for sin^2 and cos^2 are as follows:
sin^2 = (1 - cos 2x)/2
cos^2 = (1 + cos 2x)/2

so just plug n chug:

9/2*(1-cos4x) + 1/2*(1+cos4x) + 3sin4x

9/2 -9/2(cos4x) +1/2 + 1/2(cos4x) + 3sin4x

10/2 -8/2(cos4x) + 3sin4x

3sin4x -4cos4x + 5 (A=3, B=-4, C=5)

edit: i wouldn't worry about the meaning of the half- and double-angle formulas. the point is just to remember them, and use those identities when appropriate

 

[ComradeBadger]

Thats further maths surely.... (Me barfs!)

Yup, P4 is further maths, unless you do P1, P2, and M1 at AS, and P3, P4, and M2 at A2

 

[mortiz]

hey cheers =D

 

[BabyHeadCrab]

-pukes up numbers-

 

[theneb]

Quite interestering stuff, I'm going in for maths at uni in Sept. Currently doing up to P3 at alevel. My small little go started me deriving some new stuff. Cheers for the train of thought.
But that work actually doesn't seem to go past P2, except for some seeing that it's double.

 

[Prince of China]

I do grade 8 math.

 

[JimmehH]

AQA?
I'm doing that at the moment but I thought P1,P2,P4 and P5 were the bog standard A-Level (pure) modules with P3 and P6 being the further ones.
I know those are the exams I have done/about to do.

 

[Fat Tony!]

Oh god im glad we only have to do P1 P2 and P3. I feel so lucky , P1 is hard enough

 

[JimmehH]

P1's a slog. It gets better after that I think.

 

[ComradeBadger]

P2 is supposed to make P1 really easy

That's what Dave told me

 

[Naft]

so what is "P" in math terms.....i learned how to do that type of problem in my highschool trig/pre-calc class that i took this year, but what is all this P1-4 stuff, lol.

 

[Fat Tony!]

P= pure mathmatics. numbers go up in differculty.

 

[theneb]

P2 is supposed to make P1 really easy

That's what Dave told me

Well that's really what happens on anything where you advance onto higher levels, I can do P1 in my sleep now.

 

[Bad^Hat]

By the time I was in my 3rd year of High School I'd given up on Maths The teacher kept compiling a list for me of the homework I'd missed (pretty much everything), but I'd bin it when I left the class so parents didn't find it. Maths sucks, just looking at those equations brings back painful memories ;(

 

[Revisedsoul]

i used to know all that and lot more. even dabled inquantuim equations. but i got lazy

 

[sabre89]

-pukes up numbers-

lmao..............

 

[_-_-SELAS-_-_]

I can act intelligent too! E=mc²

 

[Fat Tony!]

Energy= mass* the speed of light²

 

[The Terminator]

Im in grade 12 math, were doin exponentialy growth, etc. right now.

 

[Bad^Hat]

I can act intelligent too! E=mc²

They're so cute at that age.