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 Posted: Fri Sep 15, 2006 5:18 pm
Alright, this is just a general "I've completely forgotten how to work with real trig" question. I got to this point by working through a physics problem (if you'd like to know the full problem, just say so) but the mathematical part of the question is basically solving with trig functions: cos^2 (x) - sin^2 (x) + 2 sin(x) cos(x) tan(b) = 0 Where b is a constant angle, 0<=b =b.
I have completely forgotten how to solve formulae like this. It should be very straightforward, but for some reason it's not coming to me.
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Posted: Fri Sep 15, 2006 7:11 pm
I looked some identities up because I cannot remember them.
cos(2x) = cos²(x) - sin²(x)
sin(2x) = 2 sin(x) cos(x)
So, I say [my working below in white]
cos²(x) - sin²(x) + 2 sin(x) cos(x) tan(b)
= cos(2x) + sin(2x) tan(b)
= cot(2x) + tan(b)
= tan(π/2 - 2x) + tan(b)
= 0
tan(2x - π/2) = tan(b)
I think that would help. Though, I'd be interested [maybe, sort of] in seeing the whole question.
Ironically enough, I was completely stuck in a decay width question earlier in the week because I could not remember trig identities. <_<
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Posted: Sat Sep 16, 2006 8:55 am
That seems logical. Thanks a lot; I guess it's been a while since I've really had to work with trig sweatdrop .
The entire problem is pretty basic. It's just range of a projectile, with fixed initial velocity but variable angle, fired up a hill of angle beta. Find x range and y range as a function of the angles alpha and beta (alpha being the angle of the projectile); find the angle alpha that produces maximum x-range; find maximum x-range. This problem happened to come from part 2 of 3.
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Posted: Tue Sep 19, 2006 1:23 am
All of a sudden I feel slightly better about my own inability to remember trig identities...
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Posted: Tue Sep 19, 2006 6:02 am
Dave the lost All of a sudden I feel slightly better about my own inability to remember trig identities... meh, just carry everything on a list.
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Posted: Tue Sep 19, 2006 7:50 am
poweroutage Dave the lost All of a sudden I feel slightly better about my own inability to remember trig identities... meh, just carry everything on a list. Or derive them all using complex numbers ie cos(A+B) +i sin(A+B)= exp(i*(A+B)) = exp(iA)*exp(iB) = (cosA+isinA)(cosB+isinB)= cosAcosB-sinAsinB+i*(cosAsinB+sinAcosB) then equate real and imaginary. I can't forget them though. After you teach them a few times they're hard wired.
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Posted: Tue Sep 19, 2006 10:49 am
jestingrabbit poweroutage Dave the lost All of a sudden I feel slightly better about my own inability to remember trig identities... meh, just carry everything on a list. Or derive them all using complex numbers ie cos(A+B) +i sin(A+B)= exp(i*(A+B)) = exp(iA) + exp(iB) = (cosA+isinA)(cosB+isinB)= cosAcosB-sinAsinB+i*(cosAsinB+sinAcosB) then equate real and imaginary. I can't forget them though. After you teach them a few times they're hard wired. you don't have time to derive everything on an exam. I say, cheat. edit: it's interesting that you put your equal signs after the lines, I always put my equal signs before the calculations.
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Posted: Tue Sep 19, 2006 1:17 pm
The worst ones, I think, are the half-angle formulas. The double angle formulas follow straight from the additive formulae, which aren't too hard to remember (I'm kinda mad I forgot them). But half-angle, for some reason, just hates my brain and refuses memorization or even recollection. If you showed me the wrong formula, I probably couldn't even tell the difference.
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Posted: Tue Sep 19, 2006 7:52 pm
poweroutage edit: it's interesting that you put your equal signs after the lines, I always put my equal signs before the calculations. If I was writing it down, I'd put the equal signs in a column and have everything but the first statement come after the equal signs. Its hard to write maths on these forums...
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Posted: Tue Sep 19, 2006 9:49 pm
jestingrabbit poweroutage edit: it's interesting that you put your equal signs after the lines, I always put my equal signs before the calculations. If I was writing it down, I'd put the equal signs in a column and have everything but the first statement come after the equal signs. Its hard to write maths on these forums... yeah, it's not very formatting friendly. The Guild's page of useful convertion's and couldn't be formatted in the table manner. It would be a huge asset to gaia if they incorporated a more straightforeward way of displaying such information (as would fit best in a table). It would allow people to use gaia for things they haven't yet used it for. Like for example, we're the only science and math guild on gaia, with such a tool there might be more interest based guilds requiring the ability to make diagrams/tables. or not, they might not be very interesting, erm economics and acteurial (that is so spelled wrong) sciences, but.... ok I got nothing at this point.
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Posted: Tue Sep 19, 2006 9:50 pm
Swordmaster Dragon The worst ones, I think, are the half-angle formulas. The double angle formulas follow straight from the additive formulae, which aren't too hard to remember (I'm kinda mad I forgot them). But half-angle, for some reason, just hates my brain and refuses memorization or even recollection. If you showed me the wrong formula, I probably couldn't even tell the difference. your mind is there for better things, like remembering how to go about doing proofs or what methods you need to use to solve problems, not memorizing equations. don't be mad.
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Posted: Wed Sep 20, 2006 9:08 am
My memory is awful. It's pretty annoying. I can see how I'm going to work through a question but then I get stuck because I cannot remember some trivial identity.
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Posted: Thu Sep 21, 2006 9:03 pm
That's a double-edged sword, really. Understanding proofs and how to solve problems is important, there's no doubt there. But the faculty of *actually* being able to solve the problem is also necessary; especially since we can't have calculators on the exam. Plus it's a matter of pride; I HATE being dependent on my TI-89 for these trig functions (as well as other things).
Besides, maybe my mind is there for understanding proofs and othersuch. But my memory's extraordinarily poor (even my psychiatrist says he's never seen anything like it) and things like that escape me, too.
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Posted: Fri Sep 22, 2006 3:07 am
I don't own a calculator any more: it is liberating like not owning a watch. XD
At uni we were only allowed things that could do basic sums and nothing more.
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Posted: Wed Oct 11, 2006 8:35 am
i havent brought a calculator to a maths exam in ages
that said you don't need them in topology... stupid topology stare
though i did get stuck when i came across a sequence starting with root 2 and couldnt figure out what it was converging toward. because im stupid.
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