24-12-2002 18:38									#1
	Arrg! Maths problem... Inflate your Upload Space

Ok, this questions really annoying me now. I know a lot of people here are are good at maths so i'd appreciate any help with this:

Integrate: cos(2x) / (cosx + sinx) dx

	24-12-2002 19:07									#2
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kos(2x)/(kosx+sinx)dx=(kosx+sinx/2)dx=kosx*dx+sinx/2*dx

Not sure if that is correct, I am not so good at maths...

	24-12-2002 19:18									#3
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You need the cosine addition formula. It is:

cos(x + y) = cos (x) * cos (y) - sin (x) * sin (y)

Setting x = y, we get:

cos(2x) = (cos(x))^2 - (sin(x))^2

Then we rewrite the expression:

cos(2x) / (cosx + sinx) = ((cos(x))^2 - (sin(x))^2) / (cos(x) + sin(x)) = cos(x) - sin(x)

(For the last step I used the formula (a^2 - b^2) = (a + b)(a - b).)

Now you can evaluate the integral:

(cos(x) - sin(x)) dx = cos(x) dx - sin (x) dx = sin(x) + cos(x)

	24-12-2002 20:21									#4
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Glad I ain't doing trig any more.

It's hardly Maths is it.

	24-12-2002 20:23									#5
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Aha!!!! Thanks Zero-Tau! I was just missing the last bit with (a^2 - b^2) = (a + b) (a - b).

Sometimes you just dont see these things. Thanks again

	24-12-2002 20:27									#6
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Advanced Maths is being able to do 42 x 39 in a couple of seconds, not remembering daft little formulae.

	24-12-2002 20:30									#7
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No, thats what calculators do.
Advanced maths is knowing the process from the problem to the solution.

	24-12-2002 20:36									#8
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No, that's problem-solving.

	24-12-2002 20:56									#9
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quote: Originally posted by Boddington's No, that's problem-solving.

It's all problem-solving, be it punching a calculator or actually thinking about how to tackle an integral. But only the latter is mathematical problem-solving.

	24-12-2002 20:59									#10
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Integrating x^2 to (x^3)/3 takes no mathematical skill at all in my opinion - just memory. Similarly, that cos(x + y) = cos (x) * cos (y) - sin (x) * sin (y).

A good memory can remember things like this, even if it isn't a great mathematical mind, whereas a great mathematician may have great problems remembering lists and lists of formulae.

	24-12-2002 21:13									#11
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Okay, what takes mathematical skills?

	24-12-2002 21:19									#12
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15:27.

Go and read.

	24-12-2002 22:07									#13
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Doing 42 x 39 in your head is really advanced... to a 10th grader.

	24-12-2002 22:09									#14
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..in a couple of seconds.

	24-12-2002 22:13									#15
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Yes.

	24-12-2002 22:29									#16
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Hrm...
1
42
39
---
1
378
1260
------
1638

	24-12-2002 22:32									#17
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Why in god's name are you doing trig on Xmas eve?

	24-12-2002 22:44									#18
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quote: Originally posted by mrmitchell Hrm... 1 42 39 --- 1 378 1260 ------ 1638

42 x 39 = (40 + 1) (40 - 1) +39 = 40^2 - 1 +39.

	25-12-2002 02:00									#19
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quote: Why in god's name are you doing trig on Xmas eve?

My uni (yes this is uni work, albeit only a first year refresher thingy) decided it would be a nice idea to give me 5 pieces of coursework to do over christmas. And besides christmas eve is hardly a sacred day to me... it's as good a day as any to do trig.

	25-12-2002 02:40									#20
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quote: Advanced Maths is being able to do 42 x 39 in a couple of seconds, not remembering daft little formulae.

Actually, mathematicians are notoriously bad at arithmatic.

Both 42*39 and the trig formulas can be derived through a few short tricks. Juggernaut showed how to do 42*39, and cos(2x) can be expanded quite easily if you Taylor expand the exponential fuction of ix.

Mathematicians don't try to multiply large numbers or integrate trivial functions, but investigate the nature of things like the multiplication of reals and the integration of scalar functions, and see if they can determine any interesting things from them.

	25-12-2002 03:08									#21
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quote: Originally posted by Juggernaut 42 x 39 = (40 + 1) (40 - 1) +39 = 40^2 - 1 +39.

once again... problem solving.

	25-12-2002 09:11									#22
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quote: Originally posted by Boddington's 15:27. Go and read.

First thing you need to realise that I could be in a different time zone than yours. Basic knowledge, yes?

Second thing is, you are sad if you count punching calculator or doing mental arithematic as mathematic skills.

	25-12-2002 21:56									#23
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Says the guy posting about Maths on Christmas Day.

	26-12-2002 05:53									#24
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But we forgive you for it, Bodds.

	26-12-2002 22:39									#25
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quote: Originally posted by Boddington's Says the guy posting about Maths on Christmas Day.

Do you have a problem with that?