Write a Python program that uses a while loop to compute and print the cosine of

Question

Write a Python program that uses a while loop to compute and print the cosine of an angle using the first 20 terms of the following series

cosx = 1 - ((x^2/2!)) + ((x^4/4!)) - ((x^6/6!))....

where x is in radians. Your program must input a value for x in degrees, convert it to radians and print the computed cosine of the given angle. You may use math.cos to check your answer, but do not use it in your solution!

Hint: Notice how the numerator and denominator change from iteration to iteration and apply a "rule" that will update the numerator and denominator at each iteration. Note that the numerator of each term is the numerator of the previous term multiplied by x 2 and also note the denominator of each term is the denominator of the previous term multiplied by the next two integers in the series. You should NOT re-compute the complete factorial at each step!

Constraints:

You must use while loops for all repetition in your solution to this problem, do not use for loops.

• Do not import or use any module functions to solve this problem

• Do not use the Python exponentiation operator (see Hint below)

• Do not construct or call any user-defined functions in your solution

Has to be in python

Explanation / Answer

the general term of a cosx series is (-1)(i) (x2i)/(2i)! , where i = 0 to inf

#######################################

sum = 0.0

def power(val,n):

     mul = 1

     i=0

    while(i<n):

          mul = mul*val

          i = i +1

return mul

def fact(n):

     mul = 1

     i = 1

     while (i < n+1):

          mul = mul*i

          i = i +1

return mul

x = some_value

i = 0

while (i<20):

     sum+= power(-1,i)*power(x, 2*i)/fact(2*i)

     i+=1

print sum

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