Interesting mathematics

Discus: College Confidential Café: 2004 Archive: Interesting mathematics
 By Tongos (Tongos) on Wednesday, September 08, 2004 - 09:36 pm: Edit

--math discussion----
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...

 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....

0.6534042619In{(2.6131259+x)/(2.6131259-x)}+0.2703016428In{(1.0823922+x)/(1.0823922-x)}
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.

 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

Tongos,

Where's Vancat?

 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.