The Student Room Group

Another hard C3 Q

Give it a go and if you get it, please explain. Thank you. :redface:

Scroll to see replies

Original post by hajs
Give it a go and if you get it, please explain. Thank you. :redface:


You know cos4x = 2(cos2x)^2 -1

Now expand the cos2x using the double angle formula and that should lead you to the solution
Original post by hajs
Give it a go and if you get it, please explain. Thank you. :redface:


What paper is this from? :smile:
Reply 3
miz064 is correct, but said it in an unorthodox way haha.

If you still don't get it feel free to PM.
1)
Cos4x = Cos2xCos2x - Sin2xSin2x
=(Cos2x)^2 - (Sin2x)^2
= (2cos(^2)x-1)^2 - (2sinxcosx)^2

Sub-parts:
(2cos(^2)x-1)^2 = 4cos(^4)x - 4cos(^2)x + 1
(2SinxCosx)^2 = (4)(Sin(^2)x)(Cos(^2)x) = 4(Cos(^2)x)(1 - (Cos(^2)x) = 4Cos(^2)x - 4Cos(^4)x

Stick 'em together:

(4cos(^4)x - 4cos(^2)x + 1) - (4Cos(^2)x - 4Cos(^4)x)
= 8Cos(^4)x - 8Cos(^2)x + 1
Reply 5
Original post by wizard101
You know cos4x = 2(cos2x)^2 -1

Now expand the cos2x using the double angle formula and that should lead you to the solution

Ah. Great! Thank you!

Original post by iAmanze
miz064 is correct, but said it in an unorthodox way haha.

If you still don't get it feel free to PM.


Haha i got it dw. Thank you anyway.

Original post by theDanIdentity
1)
Cos4x = Cos2xCos2x - Sin2xSin2x
=(Cos2x)^2 - (Sin2x)^2
= (2cos(^2)x-1)^2 - (2sinxcosx)^2

Sub-parts:
(2cos(^2)x-1)^2 = 4cos(^4)x - 4cos(^2)x + 1
(2SinxCosx)^2 = (4)(Sin(^2)x)(Cos(^2)x) = 4(Cos(^2)x)(1 - (Cos(^2)x) = 4Cos(^2)x - 4Cos(^4)x

Stick 'em together:

(4cos(^4)x - 4cos(^2)x + 1) - (4Cos(^2)x - 4Cos(^4)x)
= 8Cos(^4)x - 8Cos(^2)x + 1


Thank you :h:

Original post by creativebuzz
What paper is this from? :smile:

Elmwood? Heard of em? Paper D :smile:
Original post by theDanIdentity
1)
Cos4x = Cos2xCos2x - Sin2xSin2x
=(Cos2x)^2 - (Sin2x)^2
= (2cos(^2)x-1)^2 - (2sinxcosx)^2

Sub-parts:
(2cos(^2)x-1)^2 = 4cos(^4)x - 4cos(^2)x + 1
(2SinxCosx)^2 = (4)(Sin(^2)x)(Cos(^2)x) = 4(Cos(^2)x)(1 - (Cos(^2)x) = 4Cos(^2)x - 4Cos(^4)x

Stick 'em together:

(4cos(^4)x - 4cos(^2)x + 1) - (4Cos(^2)x - 4Cos(^4)x)
= 8Cos(^4)x - 8Cos(^2)x + 1


can you not post full solutions
Reply 7
Original post by gr8wizard10
can you not post full solutions


Why?
Original post by gr8wizard10
can you not post full solutions



ohhh.. that was why the miz guys' post got deleted? because he posted full solutions?

but that shouldn't be a problem, should it? i mean, once a student sees the question; he/she should be aware that the comments would contain the answer..? and shouldn't scroll down the page until the question is done or he/she is stuck?
Reply 9
I still don't understand why you cant post full solutions?

I do try to get the answer before asking people on here..
Reply 10
Original post by iAmanze
miz064 is correct, but said it in an unorthodox way haha.

If you still don't get it feel free to PM.


lol pretty much I was doing c4 so wanted to answer quickly
Reply 11
Original post by theDanIdentity
ohhh.. that was why the miz guys' post got deleted? because he posted full solutions?

but that shouldn't be a problem, should it? i mean, once a student sees the question; he/she should be aware that the comments would contain the answer..? and shouldn't scroll down the page until the question is done or he/she is stuck?


that's pretty stupid all im trying to do is help some peeps out lol
Original post by hajs
I still don't understand why you cant post full solutions?

I do try to get the answer before asking people on here..


Its because if people do post the full solution to every question, the OP wouldn't actually learn from their mistakes or where they went wrong. All post should only guide to a solution and not giving the full methods towards a solution. Although, I think there is a better reason to why you cant post a full solution but I am not too sure about it. A mod might give a better answer.

@miz064


@theDanIdentity
(edited 8 years ago)
Original post by hajs
Why?


Original post by hajs
I still don't understand why you cant post full solutions?

I do try to get the answer before asking people on here..


only give pointers and nudges to allow the student in question to derive the answer logically. creates a better learning environment, allowing students to think about each step taking into consideration what they have learnt to engrain it into their chain of thought.
Original post by hajs
Give it a go and if you get it, please explain. Thank you. :redface:


If you do further maths you could use De moivres theorem.


Posted from TSR Mobile
I did it using de moivre's theorem, expanding (cosx +isinx)^4. Though this is more FP2 than C3 :smile:
Reply 16
Original post by iPixelBlue
I did it using de moivre's theorem, expanding (cosx +isinx)^4. Though this is more FP2 than C3 :smile:


Good shout! I suppose you're doing STEP prep too? :wink:
Original post by Buses
Good shout! I suppose you're doing STEP prep too? :wink:


Yep :colondollar:
Original post by iPixelBlue
Yep :colondollar:


You sitting all 3? What do you need?


Posted from TSR Mobile
Year 12 Further Maths student here... I really feel like I've missed out on a lot of these trignonometric identities in C3. Our teacher wasn't great -_-

Could someone summarise all of the important ones here? That would be a great help...

Quick Reply

Latest