On Monday, February 20, 2017 at 2:00:03 AM UTC-6, Wally W. wrote: > On Sun, 19 Feb 2017 22:42:59 -0800 (PST), Archimedes Plutonium wrote: > > >Alright, at bare minimum I need to get this table: > > > >x y > >0 0 > >.5 .86 > >1 1 > >1.5 .86 > >2 0 > > > >Now I can come reasonably close by .1 or less, but if more than .1, the game is off > > > >So far, the best two equations for sine and cosine are these two > > > >-.4x^2 + 1.6x + .09 > > > >-.6x^2 - .3x +1 > > > >Troubles: the first gives 0 as .09, then gives .8 which is good, but gives 1.3 when I need 1. The second gives 1 at 0, good, then .7 when I need .86, then .1 when I need 0 which is acceptable. So unless I can mend the two to fit better, then I must go to a 3rd power polynomial. > > > >AP > > Actually, the best two equations for sine and cosine are these two: > y = sin(x) > y = cos(x)
Stuck in Old Math, eh, what a pity and waste.
Sine and Cosine are semicircle waves, not sinusoid, that means the derivative of sine is never cosine, nor derivative of cosine is never sine. That means the integral of sine is never cosine and the integral of cosine is never sine. So you end up in Old Math as getting everything, everything wrong about sine and cosine. It is like a person who believes in a flat earth, living, today.
The true sine function is semicircle wave whose shape is more of Y = -1.44x^2 + 2.44x
Now, if we do a integral power rule on that polynomial we get 1/3 * -1.44 x^3 + 1/2*2.44x^2 and for x =1 we should end up with a area of .78 = 1/4* 3.14..*1
1/3(-1.44) +1/2(2.44) = -.48 + 1.22 = .78
Your trouble, is the whole trouble that has infested and plagued Old Math-- not a single person with a gram of Logic in their heads.
When you define sine = opposite/hypotenuse, means that the unit circle radius 1 must, absolutely must define the angle 180 degrees to be the number 2, not the number pi. When you define sine = opposite/hypotenuse, your 90 degrees cannot be pi/2, but has to be 1, And 180 degrees has to be 2.
Either you change your definition of sine to read something else, or, you do what a logical person does-- recognize 180 degrees as being 2, not pi.
So, your function Y = sin(x) is a illogical hypocrite function.