Taylor series of cosx expansion in Python

Question

I want to write a function of cos(x) using the Taylor Expansion, but not using the math.factorial function. I defined the factorial of 2i as:

def factorial_two(i):
    if i < 0:
        #Handling negative numbers
        print("Error: can't compute the factorial of a negative number!")
        return None
    elif i == 0:
        #The special case i = 0
        return 1
    else:
        i = i * 2
        #The general case
        fact = 1
        while i > 0:
            fact = fact * i
            i = i - 1
        return fact

Then I defined the approximation of cosine as:

def cosine_approx(x,n):
    sum = 0 
    for i in range(0, n+1):
        sum += ((-1) ** i) * (x**(2*i)/ factorial_two(i))
        return sum

When I run this for any x and any n I always get 1.0 as the result. When I tried the exact same function for cosine_approx(x,n), but instead use the basic math.factorial(2*i) I get the correct results. So the question is, where did I go wrong with by definition? Or am I not using it correctly? Thank you in advance.

Answer 1

your code has an error you put return sum in the for loop!! so sum always be 1.0 and returend. you should put that out of for loop.

for i in range(0, n+1):
    sum += ((-1) ** i) * (x**(2*i)/ factorial_two(i))
return sum

like that.