A different way to generate sines and cosines using a rotation matrix (sounds scary but it's not)

Pins used are for an Espruino board.

//Using a rotation matrix to generate sin and cos values
//output them on Pin A4 and input them on Pin A1 as analog values.
//Pin A4 is wired to Pin A1 for this test

A1.mode('analog');
A4.mode('analog');
//console.log(A1.getMode());
//console.log(A4.getMode());

//for angles <5 degrees sin(a)=a, where a is in radians
var s=6.28/360;
//cos^2 = 1-sin^2
var b=1.0-s*s;
// the cos
var c=Math.sqrt(b);
// a unit vector point along positive x axis
var ss=0.0;
var cc=1.0;
var sss=ss;
var ccc=cc;

for(i=0;i<361;i+=1){
//sin values
 analogWrite(A4,0.5+ss/2.0);
 console.log(i,' ',0.5+ss/2.0,' ',analogRead(A1));
//cos values
// analogWrite(A4,0.5+cc/2.0);
// console.log(i,' ',0.5+cc/2.0,' ',analogRead(A1));

//Matrix multiply the unit vector times the rotation matrix
//                       [c,-s]
// [ccc,sss] = [cc,ss] * [s, c]
//
 ccc=c*cc-s*ss;
 sss=s*cc+c*ss;
 ss=sss;
 cc=ccc;
}//next i

And some of the output:

>echo(0);
0   0.5   0.50098420691
1   0.50872222222   0.50928511482
2   0.51744178999   0.51783016708
3   0.52615604967   0.52661936369
4   0.53486234924   0.53565270466
5   0.54355803908   0.54468604562
6   0.55224047282   0.55298695353
7   0.56090700813   0.56226443884
8   0.56955500750   0.57032120241
9   0.57818183907   0.57935454337
10   0.58678487742   0.58814373998
11   0.59536150437   0.59693293659
12   0.60390910979   0.60547798886
13   0.61242509236   0.61329060807
14   0.62090686040   0.62232394903
15   0.62935183263   0.63062485694
16   0.63775743899   0.63868162050
17   0.64612112138   0.64747081712
18   0.65444033447   0.65577172503
19   0.66271254646   0.66407263294
20   0.67093523984   0.67237354085
21   0.67910591219   0.68018616006
22   0.68722207692   0.68848706797
23   0.69528126402   0.69703212024
24   0.70328102082   0.70460059510
25   0.71121891274   0.71314564736
26   0.71909252403   0.72193484397
27   0.72689945850   0.72828259708
28   0.73463734025   0.73658350499
29   0.74230381440   0.74366369115
30   0.74989654779   0.75123216601
31   0.75741322972   0.75904478522
32   0.76485157262   0.76661326009

Nice - thanks for posting up!

I guess dividing by sqrt(ss*ss+cc*cc) would ensure that even after lots of iterations, you still kept the magnitude of the 2 numbers the same?

Numerical errors do build up because computer math is quantized. Makes one wonder if the world is really a computer simulation with Plank's constant being the bit size.