import math import numpy as np import matplotlib pyplot as plt def sin

  • Anonymous
  • Python
  • 17 Feb 2020 
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import math

import numpy as np

import matplotlib.pyplot as plt





def sin_taylor(x):

    """Return the sine of x value using Taylor's series with

true estimated error e = 0,000001.



Keyword arguments:

x -- angle value (measured in degrees)"""



    sign = 1

    if x < 0:

        sign = -1

    elif x == 0:

        return 0.0



    x = math.fabs(x)

    while math.fabs(x) > 360:

        x -= 360



    x = math.radians(x)

    sum_n = 0

    sum_prev = 0

    e = 0.000001

    n = 0



    while n < 2 or math.fabs((sum_n - sum_prev) / sum_prev) >= e:

        sum_prev = sum_n

        a_n = (-1) ** n * (x ** (2 * n + 1)) / math.factorial(2 * n + 1)

        sum_n = sum_prev + a_n

        n += 1

    return sign * sum_n





print("sin(65) using Taylor's series:", sin_taylor(65))

print("sin(65) using built-in math lib function:", math.sin(math.radians(65)), end='\n\n')

print("sin(195) using Taylor's series:", sin_taylor(195))

print("sin(195) using built-in math lib function:", math.sin(math.radians(195)))



angles_first = np.arange(-3 * np.pi, 4 * np.pi, 0.1)

angles_second = np.arange(np.pi / 2, 4 * np.pi, 0.1)

built_sin = np.sin(angles_first)

taylor_sin = [sin_taylor(math.degrees(angle)) for angle in angles_second]



rows, cols = plt.subplots()

cols.plot(angles_first, built_sin)

cols.plot(angles_second, taylor_sin)

cols.set_ylim([-4, 4])

cols.legend(["sin(x) built-in function", "sin(x) Taylor's series"])



plt.show()
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