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Things You Just Don't Get In Math Class



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  #201  
Old October 29th, 2007, 9:07 pm
UAM  Female.gif UAM is offline
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Re: Things You Just Don't Get In Math Class

If someone could help me with this I'd love them forever. OK the question is:

Show that for theta being real, Re(e to the power i theta / i + e to the power i theta) is independent of theta.

And now I've realised my love of symbols! I hope that makes sense to someone. I know it's a bit of a long shot but ah well.


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  #202  
Old October 29th, 2007, 9:14 pm
Kana  Undisclosed.gif Kana is offline
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Re: Things You Just Don't Get In Math Class

ARGH I HATE MATHS! XD

There are tons of things I don't get! But decimals are my worst enemy... stuff like rounding them up, fractions to do with decimals... algebra and gah, yeah. Lots of stuff. But basically decimals are hell.


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  #203  
Old October 30th, 2007, 4:46 pm
GenevieveS  Female.gif GenevieveS is offline
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Re: Things You Just Don't Get In Math Class

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Originally Posted by UAM View Post
If someone could help me with this I'd love them forever. OK the question is:

Show that for theta being real, Re(e to the power i theta / i + e to the power i theta) is independent of theta.

And now I've realised my love of symbols! I hope that makes sense to someone. I know it's a bit of a long shot but ah well.
The trick here is to get the imaginary number out of the denominator. OK, let's see if I can write this without symbols. To help me do that, I'm going to change your theta to T. I'm also making my divisor sign bold.

You want the real part of (e^iT)/(i+e^iT).

1. Euler's Law tells us that e^iT = cos(T )+ i*sin(T). I'm gonna drop those parens, to keep it neater. So,

(e^iT)/(i+e^iT) = (cosT + i*sinT) / (i + cosT + i*sinT)

2. Rearrange the denominator to give you an a+bi form:

(cosT + isinT)) / (cosT + (1+sinT)i)

3. Multiply both the numerator and the denominator by the conjugate of the denominator. (That means, take that a+bi on the bottom, and multiply the whole thing by (a-bi)/(a-bi)

(cosT+ isinT) * (cosT-(1+sinT)i) / (cosT+(1+sinT)i)*(cosT-(1+sinT)i)

4. Simplify. The denominator is easy, because (a-bi)(a+bi)= a^2 + b^2. The numerator, I think you just have to multiply it all out.

cosT^2+icosTsinT-icosT(1+sinT)+sinT(sinT+1) / cosT^2+(sinT+1)^2

5. Simplify further multiplying out anything still to multiply

cosT^2+icosTsinT-icosT-icosTsinT+sinT^2+sinT/cosT^2+sinT^2+1+2sinT

6. Well, lookee there, I've got some things cancel each other out! Simplify still further.

cosT^2-icosT+sinT^2+sinT/cosT^2+sinT^2+1+2sinT

7. Remember that cosT^2+sinT^2=1 for any real T.

1-icosT+sinT / 1+1+2sinT

8. Let's get all our like terms combined again and get the numerator back into that a+bi form.

1+sinT-icosT / 2+2sinT

9. Any time you have a fraction, (c-d)/z = c/z - d/z. So,

((1+sinT) / (2+2sinT)) - icosT/ (2+2sinT)

10. We only care about the real part, so we can drop that last fraction.

Re(((1+sinT) / (2+2sinT)) - icosT/ (2+2sinT)) = 1+sinT / 2+2sinT

11. Factor a 2 out of the denominator

1+sinT / 2(1+sinT)

12. Cancel the 1+sinT's.

1 / 2.

So, for any real T, Re(e^iT)/(i+e^iT) = 1/2.

Whew, that may be impossible to read without symbols.... Hope it helped.


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  #204  
Old October 30th, 2007, 7:47 pm
UAM  Female.gif UAM is offline
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Re: Things You Just Don't Get In Math Class

My eyes are going all funny!

Thanks for that, I had a flash of inspiration on the train and managed to figure it all out. Good thing I got the same answer as you.


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  #205  
Old October 30th, 2007, 10:26 pm
SecretAgentZero  Undisclosed.gif SecretAgentZero is offline
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Re: Things You Just Don't Get In Math Class

And that's from WHAT Math class? I got lost trying to comprehend it.
For me, when I don't get what my math teacher is saying, I just space out by playing that Puzzle Pack game thingy on the school's calculators.


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  #206  
Old October 30th, 2007, 10:55 pm
UAM  Female.gif UAM is offline
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Re: Things You Just Don't Get In Math Class

Well I'm doing it in a first year maths course at university (I'm actually in second year but needed a subject, why I chose maths I'll never know) but you could do that sort of stuff in an advanced maths class at secondary school.


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  #207  
Old October 31st, 2007, 8:40 pm
GenevieveS  Female.gif GenevieveS is offline
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Re: Things You Just Don't Get In Math Class

Quote:
Originally Posted by SecretAgentZero View Post
And that's from WHAT Math class? I got lost trying to comprehend it.
For me, when I don't get what my math teacher is saying, I just space out by playing that Puzzle Pack game thingy on the school's calculators.
Honestly, most of that is arithmetic, especially if you think of "i" as just a variable. There's some algebra -- multiplying out (a+bi)(c+di) type things. There's some trig--the rules about sin(T) and cos(T). And I don't remember when we learned about i and e and Euler's law...might have been Algebra III/Precalculus.

It would be much easier to comprehend written with actual math symbols and spacing....

Glad you got it on your own UAM -- I'm a math geek, I actually enjoyed figuring that out!


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  #208  
Old October 31st, 2007, 8:47 pm
UAM  Female.gif UAM is offline
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Re: Things You Just Don't Get In Math Class

My only real problem with maths is that I can't just accept something. I always want to know why this is like this and why that. I want them to prove to me where they are getting it all from. So it means I spend longer trying to figure that out than the actual problems.


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  #209  
Old October 31st, 2007, 11:22 pm
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Re: Things You Just Don't Get In Math Class

Quote:
Originally Posted by SecretAgentZero View Post
For me, when I don't get what my math teacher is saying, I just space out by playing that Puzzle Pack game thingy on the school's calculators.
I think I would have learnt a lot more in math class if it wasn't for those games!


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  #210  
Old October 31st, 2007, 11:48 pm
SecretAgentZero  Undisclosed.gif SecretAgentZero is offline
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Re: Things You Just Don't Get In Math Class

Quote:
Originally Posted by Raven_Girly View Post
I think I would have learnt a lot more in math class if it wasn't for those games!
Same here. My personal bests so far:
Block Dude=Level 6(I can't figure out how to solve Level 7)
Pegs=Level 10 or so
Dino Puzzle=I HATE THIS ONE. I never play it.
That other one=
-Endless Mode=score of 2500 or so
-Puzzle Mode=Level 13


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  #211  
Old November 1st, 2007, 2:03 am
padfoots_luv  Female.gif padfoots_luv is offline
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Re: Things You Just Don't Get In Math Class

Sinusoidal functions are my kryptonite. Urgh


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  #212  
Old November 1st, 2007, 3:05 am
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Raven_Girly  Female.gif Raven_Girly is offline
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Re: Things You Just Don't Get In Math Class

Quote:
Originally Posted by SecretAgentZero View Post
Same here. My personal bests so far:
Block Dude=Level 6(I can't figure out how to solve Level 7)
Pegs=Level 10 or so
Dino Puzzle=I HATE THIS ONE. I never play it.
That other one=
-Endless Mode=score of 2500 or so
-Puzzle Mode=Level 13
That's cool! I don't remember my exact scores but I do know that Block Dude was my favourite.

Anywho back on topic, in Calculus, I always struggled with integration. I was okay with differentiation but I found integration a lot harder to grasp. I hated those problems where you had to find the area under/over/around a curve. They drove me mental.


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  #213  
Old November 2nd, 2007, 12:05 am
SecretAgentZero  Undisclosed.gif SecretAgentZero is offline
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Re: Things You Just Don't Get In Math Class

Finally I'm starting to get what my teacher's teaching in Algebra II.
But, that doesn't mean I can't stop playing Block Dude.


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  #214  
Old November 2nd, 2007, 1:02 am
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Re: Things You Just Don't Get In Math Class

I don't get long division when there's an X variable in it. Like this:

(x - 3) / (9x^2 + 6x + 15)

I can only doing it using synthetic division. Long division of this stuff drives me crazy. I just don't get it.


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  #215  
Old November 3rd, 2007, 8:38 pm
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Re: Things You Just Don't Get In Math Class

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Originally Posted by Spirit View Post
I don't get long division when there's an X variable in it. Like this:

(x - 3) / (9x^2 + 6x + 15)

I can only doing it using synthetic division. Long division of this stuff drives me crazy. I just don't get it.
I did this in Alg.II last year I think, but I don't ever remember doing a problem where the equation with the higher degree was outside of the little division thingy (yes, such a mathematical term, I know )...are you sure it wasn't (9x^2 + 6x + 15)/(x - 3)? I could do that, but I think that the answer to (x - 3) / (9x^2 + 6x + 15) would involve fractions and negative exponents or other messy stuff, we never did any of those. Here's the work for (9x^2 + 6x + 15)/(x - 3), I suppose that even if it's the wrong problem, the concept would be the same.


Here's a link to the solution cause wrote it out...with all the symbols and such. Excuse the bad handwriting, it's not that horrible with a pen and paper instead of a Wacom tablet. I could try to clarify more if the way I explained it is confusing.
http://i68.photobucket.com/albums/i2...divofpolys.jpg

PS: I really like the song that's in your sig.

PPS:
Quote:
Originally Posted by GenevieveS View Post
Honestly, most of that is arithmetic, especially if you think of "i" as just a variable. There's some algebra -- multiplying out (a+bi)(c+di) type things. There's some trig--the rules about sin(T) and cos(T). And I don't remember when we learned about i and e and Euler's law...might have been Algebra III/Precalculus.

It would be much easier to comprehend written with actual math symbols and spacing....

Glad you got it on your own UAM -- I'm a math geek, I actually enjoyed figuring that out!
I have HRS Precalc now, and we just started doing stuff with theta and we started talking about sine and cosine...hopefully it's just the computer symbols that are making it look confusing.


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Last edited by Kitunen; November 3rd, 2007 at 8:57 pm.
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  #216  
Old November 5th, 2007, 2:31 pm
GenevieveS  Female.gif GenevieveS is offline
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Re: Things You Just Don't Get In Math Class

Quote:
Originally Posted by Kitunen View Post
I have HRS Precalc now, and we just started doing stuff with theta and we started talking about sine and cosine...hopefully it's just the computer symbols that are making it look confusing.
One thing that helped me with theta and trig functions is to remember that "Theta" is just a symbol...and it can stand for anything. Even an expression like (X+3Y). We started trig functions around this time of year, too, because I still remember my teacher talking about "sine of pumpkin" and "cosine of pilgrim hat" to help us not be so scared of the greek letters....Good luck!


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  #217  
Old November 5th, 2007, 7:07 pm
FlyingPotato  Female.gif FlyingPotato is offline
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Re: Things You Just Don't Get In Math Class

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Originally Posted by GenevieveS View Post
One thing that helped me with theta and trig functions is to remember that "Theta" is just a symbol...and it can stand for anything. Even an expression like (X+3Y). We started trig functions around this time of year, too, because I still remember my teacher talking about "sine of pumpkin" and "cosine of pilgrim hat" to help us not be so scared of the greek letters....Good luck!
My math teacher always calls functions "that dude"
He also told us the "X^n" functions were the All Blacks, exponential some rocking dude and natural logarithm some arrogant dude who didn't show off as much when the All Blacks were around...


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  #218  
Old November 5th, 2007, 8:00 pm
UAM  Female.gif UAM is offline
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Re: Things You Just Don't Get In Math Class

I always hated teachers saying things like that, it never helped me at all.

Currently I am hating maths. I seem to figure things out a bit too late for when the tests are but a couple of days after them I know how to do everything. It also doesn't help that some of the questions don't make it very clear (at least to me) what they're wanting me to do.


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  #219  
Old November 5th, 2007, 8:17 pm
FlyingPotato  Female.gif FlyingPotato is offline
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Re: Things You Just Don't Get In Math Class

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Originally Posted by UAM View Post
I always hated teachers saying things like that, it never helped me at all.

Currently I am hating maths. I seem to figure things out a bit too late for when the tests are but a couple of days after them I know how to do everything. It also doesn't help that some of the questions don't make it very clear (at least to me) what they're wanting me to do.
I know exactly what you mean... Last year everytime I had a math test, a few days after I was all like "OF COURSE! How stupid am I!". And, most of the time you think you've understand everything, but you can't do it on your own :/
What's difficult with math is knowing how to start.


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  #220  
Old November 5th, 2007, 8:32 pm
UAM  Female.gif UAM is offline
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Re: Things You Just Don't Get In Math Class

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Originally Posted by FlyingPotato View Post
I know exactly what you mean... Last year everytime I had a math test, a few days after I was all like "OF COURSE! How stupid am I!". And, most of the time you think you've understand everything, but you can't do it on your own :/
What's difficult with math is knowing how to start.
I know! That's exactly my problem. I just need a nudge in the right direction and more often than not I can go from there by myself (just might take me a while) but when I'm left I don't have a clue. That is my current state of mind because of this stupid homework.

If someone could tell me what this is question is asking me then that'd be a step in the right direction:

By expressing 7Pi/12 as an appropriate sum, find exact expressions for the since and cosine of 7Pi/12.


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