|By Tongos (Tongos) on Wednesday, September 08, 2004 - 09:36 pm: Edit|
Can somebody help me find an alternate form of sinx? (without using the taylor series, think of it yourself)
-----this is not a homework question.
|By Thermodude (Thermodude) on Wednesday, September 08, 2004 - 09:40 pm: Edit|
hmmm...I'm guessing you would mean a non-trigonometric form of sinx...
...good question...i'll think about it.
|By Tongos (Tongos) on Wednesday, September 08, 2004 - 09:43 pm: Edit|
yeah, thats it, thermodude.
|By 301aish (301aish) on Wednesday, September 08, 2004 - 10:20 pm: Edit|
Lol I think thats impossible--
sin(x) is by def a relationship between angles and sides, which makes it trignometric
|By Thermodude (Thermodude) on Wednesday, September 08, 2004 - 10:31 pm: Edit|
well..I was just referring to not using something like cos (90 - x) or something...which would be sorta cheap.
You can express sin(x) with just the variable x and some coeficients using the taylor series...which just makes it an infinte series...so it wouldn't suprise me if there were some other expression using just x that could represnt sin(x).
|By Tongos (Tongos) on Wednesday, September 08, 2004 - 11:25 pm: Edit|
no its not impossible, im finding the series now guys, and i found something fascinating....
this is an approximation formula for arcsinx, and could get the approximation even closer to arcsinx by my series. i just thought of it now, and its pretty cool.
any questions about the series, id be glad to answer.
|By Tongos (Tongos) on Wednesday, September 08, 2004 - 11:28 pm: Edit|
if one can find the formula for the relationship between sides and angles, one can obviously find a relationship between angles and sides.
|By Browninfall (Browninfall) on Wednesday, September 08, 2004 - 11:57 pm: Edit|
|By Ubercollegeman (Ubercollegeman) on Thursday, September 09, 2004 - 04:00 am: Edit|
It would not shock me at all to find that manipulations of the Maclaurin expansion for e^x could yield very good approximations of sinx, but I have hours of homework to do, so..maybe tomorrow .
|By Ubercollegeman (Ubercollegeman) on Thursday, September 09, 2004 - 04:49 pm: Edit|
Oh, yes, I almost forgot.
One of the impressive forms of sinx is Euler's manipulation of it to yield his infamous solution to the Basel problem.
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