Ex 5.ipynb

Kernel: Python 3 (Anaconda 5)

###### Ex 5: Calculating a series expansion

#import numpy #as np #imports the numpy maths function as a more easily called name
import math

x = input("Please input a value for x (in degrees): ")

x2 = int(x) #converts user input to an integer

xrad = math.radians(x2) #converts the inputted value to radians

ucos = 1 - ((xrad**2)/math.factorial(2)) + ((xrad**4)/math.factorial(4)) + ((xrad**6)/math.factorial(6)) #series expansion of cos(x) to 4 terms

mcos = math.cos(xrad) #calculated value

cosdiff = ucos - mcos #absolute difference between both cos values

cosper = cosdiff/((ucos + mcos)/2)*100 #percentage difference between both values

print("Value calculated using a series expansion of cos(x) with 4 terms:",ucos, '\n',
      "Value calculated using a cosine function:",mcos, '\n',
      "Absolute difference between both results:",cosdiff, '\n',
      "Percentage difference between both results:",cosper)

#The 4 term expansion of cos(x) has a negligible difference compared to cos(x) as an infinite expansion

Please input a value for x (in degrees): 

Value calculated using a series expansion of cos(x) with 4 terms: 0.5036278376714493 
 Value calculated using a cosine function: 0.5000000000000001 
 Absolute difference between both results: 0.003627837671449141 
 Percentage difference between both results: 0.7229448078814174