##Create a function that will perform the following calculation on a given input value:  ?=5sin(?−6?12) . (The input value here is  ? , and  ?=3.14159...  is a constant.)
import math  
from sympy.abc import x

def sin_f(x):
    y =  5 * math.sin((x-6*math.pi)/12)
    return y

print(sin_f(math.radians(95)))

##Complete the loop below to create a list named "x_list" that contains values ranging from 0 to 100, incremented by 0.25 (i.e.; 0, 0.25, 0.5, ... 99.5, 99.75, 100). Print out the list after creating it.
x_list = []

maxCount = 100
count = 0
while(count < maxCount):
    x_list.append(count)
    count = count + 0.25
    
print(x_list)

##Now create "y_list", which contains the value  ?  as defined in your function, given the  ?  values from "x_list". Then, print the first value of "y_list".
y_list = []
i = 0
for i in range(len(x_list)):
    
    y = 5 * math.sin((x-6*math.pi)/12)
    y_list.append(y)
    i = i + 1
    
print(y_list[1])

##Run the cell below to plot "x_list" against "y_list". Don't worry about understanding what that code is doing just yet. We will get to plotting later.
%pylab inline
import matplotlib.pyplot as pl

pl.plot(x_list,y_list)
pl.xlabel('x')
pl.ylabel('y')
pl.show()

##Create a new function called "y_from_list" that takes in an entire list of  ?  values as input, and then calculates all of the corresponding  ?  values and returns a list of those  ?  values.
def y_from_list(input_list):
    output_list = []
    for j in range(len(input_list)):
        output_list.append(y_from_list)
    return output_list
  
##If the function you just wrote is working properly, it should run the following cell:
  y_list2 = y_from_list(x_list)

pl.plot(x_list,y_list,ls=':',linewidth=3,label='y_list')
pl.plot(x_list,y_list2,linewidth=1,label='y_list2')
pl.xlabel('x')
pl.ylabel('y')
pl.legend()
pl.show()