-- This program uses Euler's algorithm to solve the simultaneous
-- ordinary differential equations for the sine and cosine.  The
-- interval of integration is from zero to one.

local s=0 -- sine starts at zero
local c=1 -- cosine starts at one
local n=1e9 -- 1e9 steps
local h=1/n -- size of one step
local sNew -- a temporary location
local cNew -- another temporary location

	for j=1,n do
	sNew=s+c*h
	cNew=c-s*h
	s=sNew
	c=cNew
	end

print( s,c )