""" Hello Peter, 
    this is your test of the Taylor series for sin(x)
"""

# import some tools to make life easier
import numpy as np                 # np.pi means 3.1415.., np.sin(x) is Sinus
import matplotlib.pyplot as plt    # use plt to plot something on the screen

print("Here is Taylor.py")

# Just a test for an angle of 10 degree
x_degree = 10.0      
x        = x_degree * np.pi / 180.  # convert to radian
print("x_degree =", x_degree )
print("x        =", x )             # x radian
print("x-x**3/6 =", x - x**3 / 6. ) # first terms of Taylor expansion of sin(x)
print("sin(x)   =", np.sin(x) )     # full precision sinus

# plot sinus and the first approximations of a Taylor expansion
# a list of angles between 0 and 120 degree in steps of 5 degree
xl_degree = np.arange( 0.0, 120.0, 5.0 )    # creates a list of numbers
xl        = xl_degree * np.pi / 180.        # converts to radian

plt.clf()                                 # remove previous plot (if existing)
print("Sinus(x) is blue.")
plt.plot(xl, np.sin(xl) ,   'b-')         # b =blue,    - = simple line
plt.plot(xl, xl,            'r:')         # r = red     : = dotted
plt.plot(xl, xl - xl**3/6., 'g-.')        # c = cyan   -. = dash/dott
plt.plot(xl, xl - xl**3/6., 'g*')         # g = green,  * = stars
plt.xlabel("angle [radian]")
plt.ylabel("Taylor of sin(x)")
plt.show()                                # display result of plt.plot commands