Maths Core 4 Revision Help

Ricochet J

Ricochet J

Ricochet J

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Joined
29 Jun 2004
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Hello. I need help. I know the following trig identities:

cos²A + sin²A = 1
1 + tan² A = sec² A

cos2A = 2cos²A - 1 = cos² A = 0.5(1 + cos2A)
cos2A = 1 - 2sin²A = sin²A = 0.5(1 - cos2A)
sin2A = 2sinAcosA

sin(A +/- B) = sinAcosB +/- cosAsinB
cos(A +/- B) = cosAcosB -/+ sinAsinB

Here's where the problem starts. I want to integrate the following:

1/ tan²x dx
2/ cos²3x dx
3/ sin3xcos3x dx
4/ sin²0.5x dx

Now the book i'm working from managed to convert the above using the idendities to:

1/ sec²-1 dx
2/ 0.5(1 + cos6x)
3/ 0.5sin6x
4/ 0.5(1 - cosx)

I can happily do the integrals no probs. But HOW THE HELL did they convert from the first set of integrals to the second ONLY using the above identities. I'm well and truely baffled.

Thanks! :)
 
1/ uses 1 + tan²x = sec²x, it just moves the +1 to the other side, giving tan²x = sec²x - 1.

2/ uses cos²x = 0.5(1 + cos2x), the example given is just the same but 3 times bigger.

3/ uses sin2x = 2sinxcosx, the example given is just the same but with different coefficients.

4/ uses sin²x = 0.5(1 - cos2x), the example given is just the same but divided in half.
 
Last edited:
Calder said:
1/ uses 1 + tan²x = sec²x
2/ uses cos²x = 0.5(1 + cos2x)
3/ uses sin2x = 2sinxcosx
4/ uses sin²x = 0.5(1 - cos2x)
Click to expand...

this man looks like hes got it,

im half way through my engineering degree and i still don't know any of them luckily i get a book in my exams :p
 
Nzyme said:
this man looks like hes got it,

im half way through my engineering degree and i still don't know any of them luckily i get a book in my exams :p
Click to expand...

Aye trig identities have to be what I hate most about the maths in my degree. :(
 
Calder said:
1/ uses 1 + tan²x = sec²x, it just moves the +1 to the other side, giving tan²x = sec²x - 1.

2/ uses cos²x = 0.5(1 + cos2x), the example given is just the same but 3 times bigger.

3/ uses sin2x = 2sinxcosx, the example given is just the same but with different coefficients.

4/ uses sin²x = 0.5(1 - cos2x), the example given is just the same but divided in half.
Click to expand...



Thanks for that! You've put a smile on my face! Thanks! :)

And away I go to integrate...
 
Ricochet J said:
Thanks for that! You've put a smile on my face! Thanks! :)

And away I go to integrate...
Click to expand...

Thanks for posting it, I'm meant to be revising so answering threads like this make me feel less guilty. :p
 
Nzyme said:
im half way through my engineering degree and i still don't know any of them luckily i get a book in my exams :p
Click to expand...

I'm half way through a maths degree and don't know them. Easy to work them out though - I can use them when I need them - I just couldn't read them out off the top of my head.

Enjoy integration, it's FUN!
 
Aye all depends what you've done really, I know in a couple of years I'll think of the stuff I hate just now as easy.

Differential equations are worse as well. :mad:
 
Ricochet J said:
Nah it isn't is it. What I hate is Trigo! It ****** me off so much I was want to shove a triangle up it's arse! :p
Click to expand...

If my exam turned out to be 100% trigonometry I don't think I would be able to stop myself getting up and dancing.

Like when I went into my Electronic Engineering exam (Uni level apparently) and the first question was "find the equivalent resistance of this circuit" and just had a few resistors in series/parallel. :D
 
Rebelius said:
Differential Equations = integration... no?
Click to expand...

some times

partial differential equations u end up with fourier series and stuff, gives me nightmares
 
Not exactly on topic, but it's close enough. Does anyone here use this piece of freeware :-

Eigenmath

I keep it on, and run it from, my flash drive as it requires no installation at all and just runs from the small .exe!
 
yeah - PDE's are a whole different kettle of fish :(

I did a project on something about them last year...

Fourier Series weren't much fun either.

There are some parts of maths I just love though - ODE's are one of them, Graph Theory, Programming, Geometry are others. :)
 
Azagoth said:
Not exactly on topic, but it's close enough. Does anyone here use this piece of freeware :-

Eigenmath

I keep it on, and run it from, my flash drive as it requires no installation at all and just runs from the small .exe!
Click to expand...

just a calculator with builit in functions ? looks quite useful
 
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