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#On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Date : 03/008/10
#version :2.6

"""
maclaurin_cos_2x is a function to compute cos(x) using maclaurin series
and the interval of convergence is -inf < x < +inf
cos(2x) = 1- 2^2*x^2/2! + 2^4*x^4/4! - 2^6*x^6/6! ...........
"""

from math import *

def maclaurin_cos_2x(value,k):
"""
Compute maclaurin's series approximation for cos(2x).
"""

global first_value
first_value = 0.0

#attempt to Approximate cos(2x) for a given value
try:
for item in xrange(4,k,4):
next_value = (2**item)*(value*pi/180)**item/factorial(item)
first_value += next_value

for item in xrange(2,k,4):
next_value = -1*(2**item)*(value*pi/180)**item/factorial(item)
first_value += next_value

return first_value +1

#Raise TypeError if input is not a number
except TypeError:
print 'Please enter an integer or a float value'

if __name__ == "__main__":

maclaurin_cos_2x_1 = maclaurin_cos_2x(60,100)
print maclaurin_cos_2x_1
maclaurin_cos_2x_2 = maclaurin_cos_2x(45,100)
print maclaurin_cos_2x_2
maclaurin_cos_2x_3 = maclaurin_cos_2x(30,100)
print maclaurin_cos_2x_3

######################################################################FT python "C:\
#urine series\M
#-0.5
#0.0
#0.5

#### Diff to Previous Revision

--- revision 1 2010-08-03 11:52:46
+++ revision 2 2010-08-03 12:23:33
@@ -7,7 +7,7 @@
"""
maclaurin_cos_2x is a function to compute cos(x) using maclaurin series
and the interval of convergence is -inf < x < +inf
-cos(x) = 1- 2^2*x^2/2! + 2^4*x^4/4! - 2^6*x^6/6! ...........
+cos(2x) = 1- 2^2*x^2/2! + 2^4*x^4/4! - 2^6*x^6/6! ...........
"""

from math import *