First Order Differentiation ProlemWatch

#1
As I don't like latex - I've put the question in a word file.

I'm a bit lost as to why I'm having a problem here - presumably I'm meant to use a double angle formula somewhere to get the x to x/2, but I can't figure out when.

Hope someone can help
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11 years ago
#2
differentiate?
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11 years ago
#3
You need to change

(integral of cosecx) into something that looks like the answer they give. (If you look in the edexcel formula book, its a standard manipulation of this integral)

and then apply the conditions given.

I dont understand where you're getting tan 90 from.
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#4
yeah - I know that's what I need to change. I just don't know how though
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11 years ago
#5
Have a go..... Post up your attempt.
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#6
It takes me about 10 mins to mess around with equation editor - I'm working on a mac, and everything takes 10x as long.

Will put up my workings soon
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11 years ago
#7
You could try using latex.

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#8
I've just come back to working on this one.

insparato - I'm exactly at the stage where I've got:
-e^-y=-ln(cosecx +cotx) + c

and I agree that I need to mess around with the ln part.

But through the notes that I've created - nothing has worked, and putting all this mess into equation editor would take too long.

If I split them apart, I'm still unsure how to get from x to x/2 as no formula I can remember appears to help me.
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11 years ago
#9
I can see where you would be getting tan(pi/2), but it's in the form cot(pi/2), hence is well defined.

I suggest you make the effort to learn latex, it is worth it in the long run.
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11 years ago
#10
-ln |cosecx + cotx|

Look at the trig functions inside the log. Try rearranging (cosecx + cotx) and dont forget theres a minus sign outside the log.

I'm not asking you put this all through your equation editor. You're stuck on a specific part, rearranging to

Start messing around with trig functions. sinx and cosx can be changed into half angle formula....

If you dont want to use latex, you can still adequately communciate the mathematics by using brackets and +,-,/,x,^
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11 years ago
#11
(Original post by studienka)
I've just come back to working on this one.

insparato - I'm exactly at the stage where I've got:
-e^-y=-ln(cosecx +cotx) + c

and I agree that I need to mess around with the ln part.

But through the notes that I've created - nothing has worked, and putting all this mess into equation editor would take too long.

If I split them apart, I'm still unsure how to get from x to x/2 as no formula I can remember appears to help me.
[inspirato, sorry about mowing on your lawn, I happen to be online].

plus y=0, x = pi/2 into

e^-y=ln(cosecx +cotx) + d

you get 1 = ln(1) + d so d = 1.

hence 1-e^-y = -ln|cosecx + cotx|

what can you do with the -1 infront of the ln?
have you seen the identities:

tan x = 2t/(1-t^2)
sin x = 2t/(1+t^2)
cos x = (1-t^2)/(1+t^2)

where t = tan(x/2)
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#12
I've not come across those identites b4 i don't think - where are they from?

I'm happy with everything up to this point though. Are the identities derivations from C3 double angles?

I do need to learn Latex though, I didn't find the thread on it that helpful though.
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11 years ago
#13
No probs Dirac Delta Function, incidentally ive just been doing some work on the dirac delta function myself .

What happens when you half the angle?

(1+cosx) again try looking at the cosine double angle formula specifically

I dont think he will have come across the t substitution formula Dirac Delta Function.

The threads only an introduction there is more on the wiki page which i believe is linked to the thread, trig formula can be simple put into the latex tags, like sinx ... cosx..

$sinx$

You could have a bash about using the preview post button.
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11 years ago
#14
Im not familiar with the modern A level syllibus, but they were there when I was doing A levels.

you get them from the double angle formulae:

and cos is just one divided by the other.
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11 years ago
#15
(Original post by insparato)
No probs Dirac Delta Function, incidentally ive just been doing some work on the dirac delta function myself .

What happens when you half the angle?

(1+cosx) again try looking at the cosine double angle formula specifically

I dont think he will have come across the t substitution formula Dirac Delta Function.
Aren't you still at school?? kids these days, eh, doing advanced maths well ahead of their time, what is society coming to...
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11 years ago
#16
(Original post by Dirac Delta Function)
Aren't you still at school?? kids these days, eh, doing advanced maths well ahead of their time, what is society coming to...
Ha, Well ive finished school see just waiting for them a level results, so I've been doing Laplace transforms

Back on topic,

rearrange cosecx + cotx, So what does 1+cosx equal ? using the cosine double angle formula. Infact (1+cos2x) = cos^2x is nice thing to remember for integration purposes. Dont forget about the minus sign outside the log.

If you're still not sure where its leading, ill post up what you should get so you can learn from it . Honestly its one of them things you see and remember, i remember asking the same question about a year ago on here.
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#17
Thnx for all the help - I've got it sorted out now.

This was a much harder question than the rest of the exercise - I don't remember those trig formula's so well.
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11 years ago
#18
Okay just as long as you do understand what is going on. You need to know them trig like the back of your hand for FP1.
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11 years ago
#19
Have you seen those identities involving 't' that Dirac Delta Function posted earlier....? If not, can be written as , where and hence

If we differentiate with respect to t, then we get

Remembering that :

Thus we have,

From our defenition of t earlier, we have as required.
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