Cafe math question

Discus: College Confidential Café: 2004 Archive: Cafe math question
 By Tongos (Tongos) on Monday, August 16, 2004 - 06:56 pm: Edit

Does anyone here have their own form in terms of x for the trigonometric functions, sinx, cosx, tanx? This is what i am presently working on.

 By Tongos (Tongos) on Monday, August 16, 2004 - 08:01 pm: Edit

still working on it......

 By Rbc13 (Rbc13) on Monday, August 16, 2004 - 11:29 pm: Edit

Looks impressive, I might need to steal your idea.

 By Tongos (Tongos) on Tuesday, August 17, 2004 - 02:57 pm: Edit

this is a really interesting question, define the function of us circle. no de'moveires theory, no taylor series, gammas. have your own theory please.

 By Tongos (Tongos) on Tuesday, August 17, 2004 - 10:02 pm: Edit

heres how to find the derivative of sin(-1)x. first the arc length of part of the circle in terms of x is squareroot of int{1+(-x/(squareroot(1-x^2))^2}
which is the basic formula for the distance of part of the circle in terms of x. so simplifying this, you come up with
(1-x^2)/(1-x^2)+x^2/(1-x^2)
and this gives 1/(1-x^2) => int 1/(1-x^2) when integrated this it will give you the distance, which will be expressed in radians of part of the circle. because the arc length of the circle is directly related to the length of the circle, then it should be sin(-1)x. cause this will give arc length (radian measure) in terms of x. or something along those lines. im trying...

 By Tongos (Tongos) on Tuesday, August 17, 2004 - 10:16 pm: Edit

i forgot the squareroot by (1-x^2)

 By Tongos (Tongos) on Friday, August 27, 2004 - 12:10 am: Edit

..........and here we are.