Maclaurin/Taylor Series Calculation of Sin and Cos in Python

sin_cos_functions.py

from math import pi

# round a number (x) to nearest 10 digits
def rounded(x):
	return round(x, 10)

# get the factorial of a number (x)
# factorial(x) is the product of every number from 1 to N inclusive
def factorial(x):
	n = 1; # n is the result
	# multiply n by every number from 1 to x inclusive
	for i in range(2, x + 1):
		n *= i
	return n

""" get the result of the cos and sin formulas
    where the functions are sin(x radians) or cos(x radians),
    n is the start value (n = x for sin, n = 1 for cos), and
    i_start is the exponent and factorial base in the first term """
def computeSeries(x, n, i_start):
	iterations = 20 # iterations is twice the amount of terms to use
	multiplier = 1
	for i in range(i_start, i_start + iterations, 2): # i increases by 2 each term
		multiplier *= -1 # alternates between addition and subtraction each term
		next_term = (x**i) / factorial(i) # each term is (x^i) / i!
		n += multiplier * next_term # add or subtract from final result
	return n

# get sin of x radians
def sin(x):
	return rounded(computeSeries(x, x, 3))

# get cos of x radians
def cos(x):
	return rounded(computeSeries(x, 1, 2))

# get sin of x degrees
def sinDeg(x):
	return sin(x * pi / 180)

# get cos of x degrees
def cosDeg(x):
	return cos(x * pi / 180)

# test the functions
print(sin(pi / 6)); # 0.5
print(sinDeg(45)); # 0.7071
print(sinDeg(52)); # 0.78801

print(cos(pi / 3)); # 0.5
print(cosDeg(45)); # 0.7071
print(cosDeg(52)); # 0.615661

the code seems to break at certain values of x. sinDeg(x) gives a result > 1 at x=546 similarly cosDeg(x) gives a result > 1 at x=540
tested in Python 3.9.1
jupyter core : 4.7.0
jupyter-notebook : 6.1.6