compute sin using a taylor sereis and compare it with math.sin

compute_sin.py

#!/usr/bin/env python3
# pip install matplotlib
import math
import matplotlib
import matplotlib.pyplot as plt

def float_range(end, start=0, step=0.1):
    i = start
    while i < end:
        i += step
        yield i

def nth_sin_derivative(n, a=math.pi/2):
    if n % 4 in (2,3):
        sign = -1
    else:
        sign = 1
    if n % 2 == 0:
        function = sin
    else:
        function = cos
    return sign * function(a)

def sin(x, center=math.pi/2, term_count=5):
    if x == math.pi/2:
        return 1
    elif x == 0:
        return 0
    else:
        values = (((x - center)**i / math.factorial(i)) * nth_sin_derivative(i, a=center) for i in range(term_count))
        return sum(values)

def cos(x):
    return sin((math.pi / 2) - x)

if __name__ == '__main__':
    X = list(float_range(2*math.pi))
    Y = [math.sin(x) for x in X]
    for i in range(1, 21):
        Y_approx = [sin(x, term_count=i) for x in X]

        fig, ax = plt.subplots()

        #uncomment these to generate the graphs
        #ax.plot(X, Y, color='C1')
        #ax.scatter(X, Y_approx, color='C2')
        #fig.savefig(f'figure{i}.png')

        ax.bar(X, Y_approx, color='C2')
        ax.bar(X, Y, color='C1')

        fig.savefig(f'barplot{i}.png')