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You are not logged in. #1 20060718 20:05:04
Hypobola functions to Sine and Cosine functionsSinh(iθ)= iSin(θ) X'(yXβ)=0 #2 20060718 20:58:29
Re: Hypobola functions to Sine and Cosine functionsi've always found that trigonometry is not as hard as your maths teacher makes it out to be...so why say it is so hard? #3 20060718 22:21:08
Re: Hypobola functions to Sine and Cosine functionsGood point. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #4 20060718 23:27:32
Re: Hypobola functions to Sine and Cosine functionsSo hyperbolic functions work with i the same way that trig functions work with negatives. That is pretty cool. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20060719 03:59:24
Re: Hypobola functions to Sine and Cosine functionsHmmm.. Is the second line supposed to say cosh(iθ) = icos(θ) ??? A logarithm is just a misspelled algorithm. #7 20060719 13:09:15
Re: Hypobola functions to Sine and Cosine functionsSinh(z)+Cosh(z)=Exp(z) X'(yXβ)=0 #8 20060721 05:30:16
Re: Hypobola functions to Sine and Cosine functions
So, andWhy? Anyone know? z = x + iy, by the way Last edited by ben (20060721 05:31:47) #9 20060721 05:49:22
Re: Hypobola functions to Sine and Cosine functionsIf we assume that: Then: As required. Is this what you mean by "why"? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #10 20060722 00:44:46
Re: Hypobola functions to Sine and Cosine functionsWell, and with applied to the above gives which reduces to We now want to let x = z = x + iy. Notice that even powers of i are all negative 1 or i, odd powers are positive 1 or i, alternating. Remembering that we will easily find that gathering terms which is merely to say that It then follows that All I need do now is remind you the expansion for e^x is and you should easily see (by comparing the appropriate taylors) that And as we know e^z is an entire function, we can assume the same is true here. Now that's something that really does deserve to be called cool! Last edited by ben (20060722 08:59:52) #11 20060723 01:29:56
Re: Hypobola functions to Sine and Cosine functionsAnd... IPBLE: Increasing Performance By Lowering Expectations. #12 20060723 01:55:26
Re: Hypobola functions to Sine and Cosine functionskrassi, I've seen that expression somewhere before... but I can't remember where... ;) A logarithm is just a misspelled algorithm. #13 20060723 01:59:33
Re: Hypobola functions to Sine and Cosine functionsWhence the even famouser The 5 fundamental transcendentals, all in bed together (but no action!!) #14 20060723 07:20:51
Re: Hypobola functions to Sine and Cosine functionsSorry ben. In an attempt to write a quick post, I was too brief. We can show, as my last post did, that: But we also know that: So we can say: And so it must be that: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #15 20060724 05:46:07
Re: Hypobola functions to Sine and Cosine functions
No problem, math is fun, right?
But why should I? Where did it come from, other than the taylor series I showed?
Why? It could be, by your reasoning, that Anyway, let's not fall out in public. Others seem to have lost interest anyway. #16 20060724 06:08:36
Re: Hypobola functions to Sine and Cosine functionsa really nice thing to see (atleast when i first saw it) The Beginning Of All Things To End. The End Of All Things To Come. #17 20060724 16:41:45
Re: Hypobola functions to Sine and Cosine functionsI'm astonished to see for far you guys haven't proved what I proposed! substituding z with z will get simlified form: (2) Hence sinh(iz)=[(1)(2)]/2=isinz cosh(iz)=[(1)+(2)]/2=cosz X'(yXβ)=0 #18 20060726 03:20:16
Re: Hypobola functions to Sine and Cosine functions
Well you may be, and when I tell you why you won't like it! Last edited by ben (20060726 03:51:53) #19 20060726 04:21:11
Re: Hypobola functions to Sine and Cosine functionsI just checked on this
for real x, cosh x = cos ix, and not as you wrote (how do you get thetas and stuff in here, without using LaTex?) #20 20060726 06:36:02
Re: Hypobola functions to Sine and Cosine functionsThe top of every page has this bar: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #21 20060726 16:00:55
Re: Hypobola functions to Sine and Cosine functionsOK, my proof is true if all the properties of circular and hypobolic functions are still true when the domains are complex numbers instead of real numbers. Last edited by George,Y (20060726 16:10:15) X'(yXβ)=0 #22 20060726 16:08:54
Re: Hypobola functions to Sine and Cosine functionsI was not assuming the result. X'(yXβ)=0 #23 20060726 22:58:48
Re: Hypobola functions to Sine and Cosine functions
You're right. #24 20060727 12:50:22
Re: Hypobola functions to Sine and Cosine functionsIt doesn't matter. X'(yXβ)=0 #25 20060727 17:33:00
Re: Hypobola functions to Sine and Cosine functionsI've never read it myself, but maybe you could read Complex Analysis if you want. Don't know if it's well written, just had it on my harddisc(this is the original source, I have downloaded it and kept the source url in a file ).
Last edited by Patrick (20060727 17:33:42) 