Need help approximating sine function in python using Taylor Series

Question

I'm very new to Python, and am trying to approximate the sine function using this series.

My code looks like this:

import math
def sin(x,n):
sine = 0
for i in range(n):
    sign = (-1)**i
    sine = sine + ((x**(2.0*i-1))/factorial(2**i-1))*sign
return sine

This does not return the answer that I was hoping for, but I am very confused and can't find my mistake... or maybe I'm just going about this the wrong way entirely (as I said, I'm very new to python and to programming in general).

It seems similar to the program that I had to write a while ago to approximate pi given this series:

def piApprox(n):
pi = 0
for i in range(n):
    sign = (-1)**i
    pi = pi + 1.0/(2*i+1)*sign
return 4*pi

I don't know if that is useful in any way, but it's what I was trying to use that to figure out my sine method. Any help fixing this or pointing me in the right direction would be greatly appreciated!

How does its behaviour differ from what you expected, specifically? — Oliver Charlesworth, Mar 06 '13 at 19:25
I was expecting it to return an answer close to what math.sin(x) would return. I feel like my problem lies somewhere within the for i in range(n): portion of the code. — user2141367, Mar 06 '13 at 19:28
Ok, then you should pick a simple example input, modify your code to print out all the intermediate results, and compare them to a manual calculation. — Oliver Charlesworth, Mar 06 '13 at 19:29

John Kugelman · Answer 1 · 2013-03-06T19:36:49.657

5

The Taylor series for sin(x) is:

Taylor series for sin(x)

Comparing your code to that definition, these two parts have some errors:

x**(2.0*i-1)
factorial(2**i-1)

The minuses should be pluses, and the exponent in the factorial should be multiplication.

x**(2.0*i+1)
factorial(2*i+1)

edited Mar 06 '13 at 19:36

answered Mar 06 '13 at 19:27

John Kugelman

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score 2 · Answer 2 · answered Sep 25 '13 at 11:58

You can use the symbolic library SymPy to build your approximated function using Taylor series:

from sympy import sin
from sympy.abc import x

# creates a generator
taylor_series = sin(x).series(n=None)

# takes the number of terms desired for your generator
taylor_series = sum([next(taylor_series) for i in range(num_of_terms)])

# creates a function that calculates the approximated sine function
mysin = sympy.lambdify((x,), taylor_series)

Need help approximating sine function in python using Taylor Series

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