#!/bin/lua
require 'utils'
require 'mathlib'

local N = tonumber(arg[1]) or 16

local x1 = 0
local x2 = 2*pi
local dx = (x2-x1)/N

local y = 0
for x = x1, x2, dx do
	print(x, y)
	y = y + (sin(x) + sin(x+dx))/2 * dx
end
print('"approx"')

local y = 0
for x = x1, x2, dx do
	y = -cos(x) + 1
	print(x, y)
end
print('"sine"')

--	a = 1/(N)*(1 + sin((2*n-1)*pi/N)/sin(pi/N))
--	print(n/N, a)