import matplotlib.pyplot as plt 
import numpy as np
from scipy.stats import binom

# Actual sin function
lowerlimit = -np.pi; upperlimit = np.pi

x_values = list(np.arange(lowerlimit, upperlimit, np.pi/100))

print(x_values)

y_values = [np.sin(x) for x in x_values]

# Data obtained from poly_sin3
c_program_x_range=[-3.141593, -3.110177, -3.078761, -3.047345, -3.015929, -2.984513, -2.953097, -2.921681, -2.890265, -2.858849, -2.827433, -2.796017, -2.764602, -2.733186, -2.701770, -2.670354, -2.638938, -2.607522, -2.576106, -2.544690, -2.513274, -2.481858, -2.450442, -2.419026, -2.387610, -2.356194, -2.324779, -2.293363, -2.261947, -2.230531, -2.199115, -2.167699, -2.136283, -2.104867, -2.073451, -2.042035, -2.010619, -1.979203, -1.947787, -1.916372, -1.884956, -1.853540, -1.822124, -1.790708, -1.759292, -1.727876, -1.696460, -1.665044, -1.633628, -1.602212, -1.570796, -1.539380, -1.507964, -1.476549, -1.445133, -1.413717, -1.382301, -1.350885, -1.319469, -1.288053, -1.256637, -1.225221, -1.193805, -1.162389, -1.130973, -1.099557, -1.068142, -1.036726, -1.005310, -0.973894, -0.942478, -0.911062, -0.879646, -0.848230, -0.816814, -0.785398, -0.753982, -0.722566, -0.691150, -0.659734, -0.628319, -0.596903, -0.565487, -0.534071, -0.502655, -0.471239, -0.439823, -0.408407, -0.376991, -0.345575, -0.314159, -0.282743, -0.251327, -0.219911, -0.188496, -0.157080, -0.125664, -0.094248, -0.062832, -0.031416, -0.000000, 0.031416, 0.062832, 0.094248, 0.125664, 0.157080, 0.188496, 0.219911, 0.251327, 0.282743, 0.314159, 0.345575, 0.376991, 0.408407, 0.439823, 0.471239, 0.502655, 0.534071, 0.565487, 0.596903, 0.628319, 0.659734, 0.691150, 0.722566, 0.753982, 0.785398, 0.816814, 0.848230, 0.879646, 0.911062, 0.942478, 0.973894, 1.005310, 1.036726, 1.068142, 1.099557, 1.130973, 1.162389, 1.193805, 1.225221, 1.256637, 1.288053, 1.319469, 1.350885, 1.382301, 1.413717, 1.445133, 1.476549, 1.507964, 1.539380, 1.570796, 1.602212, 1.633628, 1.665044, 1.696460, 1.727876, 1.759292, 1.790708, 1.822124, 1.853540, 1.884956, 1.916372, 1.947787, 1.979203, 2.010619, 2.042035, 2.073451, 2.104867, 2.136283, 2.167699, 2.199115, 2.230531, 2.261947, 2.293363, 2.324779, 2.356194, 2.387610, 2.419026, 2.450442, 2.481858, 2.513274, 2.544690, 2.576106, 2.607522, 2.638938, 2.670354, 2.701770, 2.733186, 2.764602, 2.796017, 2.827433, 2.858849, 2.890265, 2.921681, 2.953097, 2.984513, 3.015929, 3.047345, 3.078761, 3.110177, 3.141593]

sin3data=[2.026120, 1.904050, 1.785049, 1.669087, 1.556133, 1.446155, 1.339122, 1.235005, 1.133771, 1.035389, 0.939829, 0.847060, 0.757050, 0.669769, 0.585185, 0.503268, 0.423986, 0.347309, 0.273205, 0.201644, 0.132595, 0.066026, 0.001906, -0.059795, -0.119109, -0.176066, -0.230697, -0.283035, -0.333108, -0.380950, -0.426589, -0.470059, -0.511389, -0.550610, -0.587754, -0.622852, -0.655934, -0.687032, -0.716177, -0.743399, -0.768730, -0.792200, -0.813841, -0.833684, -0.851759, -0.868098, -0.882731, -0.895691, -0.907006, -0.916710, -0.924832, -0.931404, -0.936457, -0.940021, -0.942128, -0.942809, -0.942094, -0.940016, -0.936603, -0.931889, -0.925903, -0.918678, -0.910242, -0.900629, -0.889869, -0.877992, -0.865030, -0.851013, -0.835974, -0.819942, -0.802950, -0.785027, -0.766204, -0.746514, -0.725986, -0.704653, -0.682544, -0.659691, -0.636125, -0.611876, -0.586977, -0.561457, -0.535349, -0.508682, -0.481488, -0.453798, -0.425643, -0.397054, -0.368061, -0.338697, -0.308992, -0.278976, -0.248682, -0.218139, -0.187379, -0.156434, -0.125333, -0.094108, -0.062791, -0.031411, -0.000000, 0.031411, 0.062791, 0.094108, 0.125333, 0.156434, 0.187379, 0.218139, 0.248682, 0.278976, 0.308992, 0.338697, 0.368061, 0.397054, 0.425643, 0.453798, 0.481488, 0.508682, 0.535349, 0.561457, 0.586977, 0.611876, 0.636125, 0.659691, 0.682544, 0.704653, 0.725986, 0.746514, 0.766204, 0.785027, 0.802950, 0.819942, 0.835974, 0.851013, 0.865030, 0.877992, 0.889869, 0.900629, 0.910242, 0.918678, 0.925903, 0.931889, 0.936603, 0.940016, 0.942094, 0.942809, 0.942128, 0.940021, 0.936457, 0.931404, 0.924832, 0.916710, 0.907006, 0.895691, 0.882731, 0.868098, 0.851759, 0.833684, 0.813841, 0.792200, 0.768730, 0.743399, 0.716177, 0.687032, 0.655934, 0.622852, 0.587754, 0.550610, 0.511389, 0.470059, 0.426589, 0.380950, 0.333108, 0.283035, 0.230697, 0.176066, 0.119109, 0.059795, -0.001906, -0.066026, -0.132595, -0.201644, -0.273205, -0.347309, -0.423986, -0.503268, -0.585185, -0.669769, -0.757050, -0.847060, -0.939829, -1.035389, -1.133771, -1.235005, -1.339122, -1.446155, -1.556133, -1.669087, -1.785049, -1.904050, -2.026120]

# Data obtained from poly_sin5
sin5data=[-0.524044, -0.521131, -0.520097, -0.520826, -0.523202, -0.527114, -0.532453, -0.539115, -0.546995, -0.555995, -0.566017, -0.576967, -0.588753, -0.601286, -0.614481, -0.628253, -0.642523, -0.657211, -0.672242, -0.687543, -0.703043, -0.718674, -0.734371, -0.750069, -0.765709, -0.781232, -0.796580, -0.811702, -0.826544, -0.841058, -0.855195, -0.868912, -0.882166, -0.894914, -0.907120, -0.918745, -0.929756, -0.940120, -0.949806, -0.958785, -0.967030, -0.974517, -0.981223, -0.987125, -0.992204, -0.996444, -0.999826, -1.002337, -1.003965, -1.004697, -1.004525, -1.003440, -1.001436, -0.998508, -0.994652, -0.989867, -0.984151, -0.977505, -0.969932, -0.961434, -0.952017, -0.941686, -0.930449, -0.918313, -0.905288, -0.891386, -0.876616, -0.860994, -0.844531, -0.827243, -0.809146, -0.790257, -0.770593, -0.750173, -0.729016, -0.707143, -0.684574, -0.661332, -0.637439, -0.612918, -0.587793, -0.562089, -0.535830, -0.509044, -0.481755, -0.453992, -0.425780, -0.397148, -0.368125, -0.338738, -0.309017, -0.278991, -0.248690, -0.218143, -0.187381, -0.156434, -0.125333, -0.094108, -0.062791, -0.031411, -0.000000, 0.031411, 0.062791, 0.094108, 0.125333, 0.156434, 0.187381, 0.218143, 0.248690, 0.278991, 0.309017, 0.338738, 0.368125, 0.397148, 0.425780, 0.453992, 0.481755, 0.509044, 0.535830, 0.562089, 0.587793, 0.612918, 0.637439, 0.661332, 0.684574, 0.707143, 0.729016, 0.750173, 0.770593, 0.790257, 0.809146, 0.827243, 0.844531, 0.860994, 0.876616, 0.891386, 0.905288, 0.918313, 0.930449, 0.941686, 0.952017, 0.961434, 0.969932, 0.977505, 0.984151, 0.989867, 0.994652, 0.998508, 1.001436, 1.003440, 1.004525, 1.004697, 1.003965, 1.002337, 0.999826, 0.996444, 0.992204, 0.987125, 0.981223, 0.974517, 0.967030, 0.958785, 0.949806, 0.940120, 0.929756, 0.918745, 0.907120, 0.894914, 0.882166, 0.868912, 0.855195, 0.841058, 0.826544, 0.811702, 0.796580, 0.781232, 0.765709, 0.750069, 0.734371, 0.718674, 0.703043, 0.687543, 0.672242, 0.657211, 0.642523, 0.628253, 0.614481, 0.601286, 0.588753, 0.576967, 0.566017, 0.555995, 0.546995, 0.539115, 0.532453, 0.527114, 0.523202, 0.520826, 0.520097, 0.521131, 0.524044]


plt.plot(x_values, y_values, label = "sin(x)")
plt.plot(c_program_x_range, sin3data, label = "Maclaurin degree 3")
plt.plot(c_program_x_range, sin5data, label = "Maclaurin degree 5")
plt.title("Maclaurin Approximations of sin(x)")
plt.legend()
plt.show()