Assistance with Lua Cosine, wrong results returned - math

Question

Ok, first up, this is NOT for a class, test, or other student type activity.
I'm a scripter for a game, and am trying to implement the math library for all to use, and unfortunately, all I have available to me is very basic lua. The implemented version cannot be changed, and does not include any libraries. For those wondering, its for scripting in Fold.It.
Here's what I have...
math={}
math.fact = function(b) if(b==1)or(b==0) then return 1 end e=1 for c=b,1,-1 do e=e*c end return e end
math.pow = function(b,p) e=b if(p==0) then return 1 end if(p<0) then p=p*(-1) end for c=p,2,-1 do e=e*b end return e end
math.cos = function(b,p) e=0 p=p or 10 for i=1,p do e=e+(math.pow(-1,i)*math.pow(b,2*i)/math.fact(2*i)) end return e end
To clarify above, math.fact returns factorial, which is returning accurate to about 10 points of precision, and is a new function I've done to aid in cosine calculation.
The math.pow is also a new function to handle returning powers, also working as expected.
The issue is with the cosine function. Its returning unexpected values. Here's an easier to digest version (I've been writing my library stuff ultra lean)...
function math.cos(value,precision)
result=0
precision=precision or 10
for i=1,precision do
result=result+(math.pow(-1,i)*math.pow(value,2*i)/math.fact(2*i))
end
return e
end
The problem is, with those functions, for print(math.cos(90)) it returns 4.77135... when I'm expecting -0.44807... (based on calc in scientific mode, or using an online tool to cos(90)).
I'm also having issues with sin and tan, however they are similarly written to cos, which seems to have been done in many languages. If I can figure out what I'm doing wrong, I can get them all fixed.
EDIT: Corrected typo

Answer 1

First, your lua doesn't run. Second, you need to make your variables local. Third, cosine starts with a one.
The problem is because the Taylor series you are using only converges on the correct values of cosine close to zero. You would have to use a far more terms of the series to get it to handle 90 correctly. You can fix this for your implementation two ways:
Add a pi constant. Then use a while loop to adjust the value such that abs(value) < 2*pi:
math.pi = 3.14159265358
while value > math.pi*2 do
value = value - math.pi * 2
end
while value < -math.pi*2 do
value = value + math.pi * 2
end
Or - find or implement a version of fmod in lua.
Here is the corrected code (you can minify it):
math={}
math.fact = function(b)
if(b==1)or(b==0) then
return 1
end
local e=1
for c=b,1,-1 do
e=e*c
end
return e
end
math.pow = function(b,p)
local e=b
if(p==0) then
return 1
end
if(p<0) then
p=p*(-1)
end
for c=p,2,-1 do
e=e*b
end
return e
end
math.cos = function(b,p)
local e=1
b = math.correctRadians(b)
p=p or 10
for i=1,p do
e=e+(math.pow(-1,i)*math.pow(b,2*i)/math.fact(2*i))
end
return e
end
math.pi = 3.1415926545358
math.correctRadians = function( value )
while value > math.pi*2 do
value = value - math.pi * 2
end
while value < -math.pi*2 do
value = value + math.pi * 2
end
return value
end
interactive lua run:
imac:~ root$ lua -i temp.lua
Lua 5.1.4 Copyright (C) 1994-2008 Lua.org, PUC-Rio
> print( math.cos( 90 ) )
-0.44807359244883
>