Sine Approximation

[Catalyst]

code:

var factorialHold : int := 0 const maxPres := 100 var ZeroSineDx : array 0 .. maxPres of real for i : 0 .. maxPres - 4 by 4     ZeroSineDx (i) := 0     ZeroSineDx (i + 1) := 1     ZeroSineDx (i + 2) := 0     ZeroSineDx (i + 3) := -1 end for var SineHold, SineN : real := 0 var sinePres : int := 9 function sinE (n : real) : real     result sin(n) end sinE function Factorial (n : int) : int     if (n = 1) or (n = 0) then         result 1     else         factorialHold := 1         for i : 1 .. n             factorialHold *= i         end for         result factorialHold     end if end Factorial function Sine (n : real) : real     SineHold := 0     if (n = 0) then         result 0     end if     for i : 0 .. sinePres         SineHold += (ZeroSineDx (i) * (n ** i)) / (Factorial (i))     end for     result SineHold end Sine View.Set ("nobuttonbar,graphics:512;512,position:300;300,offscreenonly") for k : 1 .. 12 by 2     drawfillbox (0, 0, maxx, maxy, 7)     sinePres := k     drawline (maxx div 2, 0, maxx div 2, maxy, 10)     drawline (0, maxy div 2, maxx, maxy div 2, 10)     for i : -maxx .. maxx         drawdot (i + maxx div 2, round (sinE (i / maxx * 10) * 50) + maxx div 2, 103)         drawdot (i + maxx div 2, round (Sine (i / maxx * 10) * 50) + maxx div 2, 42)     end for     View.Update     delay (200) end for

[Homer_simpson]

nice code...
+50

[gigaman]

nice pretty cool program but what does it show?

[Delos]

As the title infers...Catalyst has used some crazy maths there (factorials, possibly some level of calculus as well) so as to approximate the value of sine on a graph, starting with the function y = x.

Of course I can't tell you exactly how this works, or the applications, but I can tell you that if you exchange the assignemnts at the start of the programme thusly:

code:

ZeroSineDx (i + 1) := -1     ZeroSineDx (i + 2) := 0     ZeroSineDx (i + 3) := 1

You get cosine. This is interesting as the graph you start off with is y = -x.

[Catalyst]

http://mathworld.wolfram.com/MaclaurinSeries.html