Functional Programming: simulating sine with an (approximate) infinite series…

functions.coffee

apply = (f) ->
	args = Array.prototype.slice.call(arguments, 1)
	(x) ->
		f.apply null, args.concat x

factorial = (n) ->
	if n
		factorial(n-1)*n
	else
		1

power = (x, n) ->
	if n
		power(x, n-1)*x
	else
		1

series = (f, x) ->
	sum = 0
	for n in [0..1000]
		sum += (apply(f, x))(n)
	return sum


e = (x) ->
	series(
		(x,n) ->
			power(x,n)/factorial(n)
		x
		)

pi = 4*series((x,k) ->
				power(-1,k)/(2*k+1)
			1
		)

sin = (x) ->
	series(
		(x,n) ->
			power(-1, n)*power(x,2*n+1)/factorial(2*n+1)
		x
		)	

console.log e(1)
console.log pi
console.log sin(pi)