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Maclaurin/Taylor Series Calculation of Sin and Cos in Python
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
@nagarajasr

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@nagarajasr nagarajasr commented Jan 4, 2021

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

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