Prove cos2(x)+sin2(x) = 1
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Original post by TheJ0ker
Cannot wait to do a maths degree, the only proof I understand is the circle one 
If you're doing/ are going to do Further Maths at A Level you'll probably understand quite a few of them (i.e, the ones using complex numbers; Eulers Relation/ De Moivre and possibly even the Power Series ones - they're just generalisations of Taylors and Maclaurin really).
To be honest, even without doing a degree you can follow most of these because you actually learn quite a lot at A Level - apparently, a big portion of a degree is going back to what you learnt at A Level and understanding why it works the way it does.
Original post by TwilightKnight
If you're doing/ are going to do Further Maths at A Level you'll probably understand quite a few of them (i.e, the ones using complex numbers; Eulers Relation/ De Moivre and possibly even the Power Series ones - they're just generalisations of Taylors and Maclaurin really).
To be honest, even without doing a degree you can follow most of these because you actually learn quite a lot at A Level - apparently, a big portion of a degree is going back to what you learnt at A Level and understanding why it works the way it does.
To be honest, even without doing a degree you can follow most of these because you actually learn quite a lot at A Level - apparently, a big portion of a degree is going back to what you learnt at A Level and understanding why it works the way it does.
I just started F.maths today
looking forward to understanding the power seriesOriginal post by TheJ0ker
I just started F.maths today looking forward to understanding the power series
looking forward to understanding the power seriesI envy you... being at the start of the adventure.
.
Original post by TwilightKnight
I envy you... being at the start of the adventure.
.
.Aren't you about to start another adventure?
I envy everyone at University this year. I want my third year modules damnit, but there's a whole year of industrial placement in the way!
Original post by TwilightKnight
I envy you... being at the start of the adventure.
.
.Are you at Uni then or graduated?
As an aside: I've been swamped at work so haven't added any recent proofs to the list. I'll rectify that over the weekend at some point...
This thread is still going on........wow.....
Original post by EEngWillow
As an aside: I've been swamped at work so haven't added any recent proofs to the list. I'll rectify that over the weekend at some point...
You need to get that placed in the OP otherwise it'll be lost somewhere in the middle of this thread.
Original post by Farhan.Hanif93
You need to get that placed in the OP otherwise it'll be lost somewhere in the middle of this thread.
I agree, but I haven't got around to asking
DFranklin
.
(I think it's on page 7)
EDIT: Yes, yes it is. http://www.thestudentroom.co.uk/showpost.php?p=33782337&postcount=132
Original post by TheJ0ker
Are you at Uni then or graduated?
I'm about to start a course in something other than Maths.
I'm going to miss doing it properly - I still intend to do little bits here and there (i.e, I have books in Vector Calculus and D.Es), but Further Maths was the best subject I did - that's what I meant. You're going to love it
.Original post by TwilightKnight
I'm about to start a course in something other than Maths.
I'm going to miss doing it properly - I still intend to do little bits here and there (i.e, I have books in Vector Calculus and D.Es), but Further Maths was the best subject I did - that's what I meant. You're going to love it.
I'm going to miss doing it properly - I still intend to do little bits here and there (i.e, I have books in Vector Calculus and D.Es), but Further Maths was the best subject I did - that's what I meant. You're going to love it
.Haha. I know what you mean. Being an engineer, I should have a lot of room to be lazy in my maths at Uni, or do things that would make a mathematician cringe/cry.
However, when I get a question about finding the limit of a series, my first impulse is to check if it does actually converge. When I'm working with complex numbers I actually write the whole thing in terms of i, instead of j - we more commonly use i to denote alternating current - and switch variables in my neat writeup!
Basically, I can't help it. We were given a table of Laplace transforms, and I went down and worked out all of them myself before I would allow myself to quote the result from the table...
I'm doing the wrong degree.
Original post by EEngWillow
I'm doing the wrong degree.
I'm doing the wrong degree.
At least yours involves Maths
At most, I'll be doing stupid Statistical tests that just involve plugging numbers into a formula.
Original post by TwilightKnight
I'm about to start a course in something other than Maths.
I'm going to miss doing it properly - I still intend to do little bits here and there (i.e, I have books in Vector Calculus and D.Es), but Further Maths was the best subject I did - that's what I meant. You're going to love it.
I'm going to miss doing it properly - I still intend to do little bits here and there (i.e, I have books in Vector Calculus and D.Es), but Further Maths was the best subject I did - that's what I meant. You're going to love it
.Yeah i'm a week into A levels and it the best subject already
Is it possible? Have we tapped the well dry of proofs for this identity?
It'd be sad if that were the case.
It'd be sad if that were the case.
Original post by Farhan.Hanif93
You need to get that placed in the OP otherwise it'll be lost somewhere in the middle of this thread.
I don't know what kind of sorcery DFranklin has access to, but I now have the first post in the thread.
Which naturally means I'm claiming this whole thing as my amazing idea.
Original post by TwilightKnight
Is it possible? Have we tapped the well dry of proofs for this identity?
It'd be sad if that were the case.
It'd be sad if that were the case.
It's possible (for now). So, next up...
(Suggestions? Anyone?)
Original post by EEngWillow
Which naturally means I'm claiming this whole thing as my amazing idea.
Which naturally means I'm claiming this whole thing as my amazing idea.
And yet you quoted me in the first post where I suggested the creation of such a list so I think you'll find it was MY idea
I dont know whether this could be adapted into a proof but if we let x=cosT, y=sinT. then dy/dx=-cotT. The normal of this is tanT. drawing the line y-sinT=tanT(x-cosT) we get a line through the origin. i.e the normal of every point on this curve passes through the origin. is there some way of showing that this then gives a circle? if there is then it is another way of showing that x^2+y^2 is a constant.
Im thinking something along the lines of the curve is continuous. suppose there was a point x_1 such that x_1 is not 1 away from (0,0). Then the set of such points is non empty so has a infinium (a point touching to points which do conform.) Then this point is on the same radial line as a point from the circle of radius 1 centre (0,0) which we shall refer to as 'the circle point'.
The line of the curve at this point can be approximated by the line segment from the infinium to the preceding point. both have the same gradient (the line segments from both the ininifum and the circle point have gradient perpendicular to the radial line) and terminate at the same point therefore the points must be equal.
PS could this same argument if valid be extended to 3d for full generality?
Edit: The more I think about it the less interesting this is and the more it looks like the standard proof.
Im thinking something along the lines of the curve is continuous. suppose there was a point x_1 such that x_1 is not 1 away from (0,0). Then the set of such points is non empty so has a infinium (a point touching to points which do conform.) Then this point is on the same radial line as a point from the circle of radius 1 centre (0,0) which we shall refer to as 'the circle point'.
The line of the curve at this point can be approximated by the line segment from the infinium to the preceding point. both have the same gradient (the line segments from both the ininifum and the circle point have gradient perpendicular to the radial line) and terminate at the same point therefore the points must be equal.
PS could this same argument if valid be extended to 3d for full generality?
Edit: The more I think about it the less interesting this is and the more it looks like the standard proof.
(edited 12 years ago)
Original post by ben-smith
And yet you quoted me in the first post where I suggested the creation of such a list so I think you'll find it was MY idea
Shush, or I'll use the edit post button!
Any ideas for a similar thread? Some possible ones:
prove: -the derivative of e^x is e^x
-Euler Polyhedron formula
prove: -the derivative of e^x is e^x
-Euler Polyhedron formula
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