calculate cos(x) by summing a series
<p>I'm very new in computer programming and recently just started up on learning python. In this assignment I need to calculate cos(x) by summing the series 1 - x^2/2! + x^4/4! - x^6/6! . . .</p>

<p>How do I do this without using numpy or m.factorial? I think I'm only supposed to use a while loop. Here is my code so far</p>

<pre><code>print("INVESTIGATION OF COMPLEX INFINITE SERIES")
print("")
print("Part A: exp, cos and sin series for real value 1")
print("Using convergence criterion of 1e-20")
print("")
print("count         exp terms       sign         cos terms         sin terms")
print("----------------------------------------------------------------------")

count = 0.0 # number of terms added so far
total = 0.0 # total of terms so far
termSign = 1 
term = 1.0 # initial term
xx = 1

while abs(term) &gt; 1e-20:
    count += 1
    print("%2d   %22.16g    %2d" % (count, term, termSign))
    termSign = (-1)**(count//2)
    total = total + term
    term = term/count
</code></pre>

<p>The output of the code should look like this:</p>

<pre><code> count     exp terms          sign          cos terms 
 ----------------------------------------------------------
 1                      1      1       1.00000000000000000                                  
 2                      1      1       
 3                    0.5     -1      -0.50000000000000000                                                                                          
 4     0.1666666666666667     -1    
 5    0.04166666666666666      1       0.04166666666666666                                                                                          
 6   0.008333333333333333      1       
 7   0.001388888888888889     -1      -0.00138888888888889                                                                                      
 8  0.0001984126984126984     -1                                                                                                        
 9   2.48015873015873e-05      1       0.00002480158730159                                                                                          
10  2.755731922398589e-06      1
11  2.755731922398589e-07     -1      -0.00000027557319224                                                                                          
12  2.505210838544172e-08     -1                                                                                                    
13   2.08767569878681e-09      1       0.00000000208767570                                                                                          
14  1.605904383682162e-10      1                                                                                    
15  1.147074559772973e-11     -1      -0.00000000001147075                                                                                          
16  7.647163731819817e-13     -1                                                                                                        
17  4.779477332387386e-14      1       0.00000000000004779                                                                                          
18  2.811457254345521e-15      1                                                                                                            
19  1.561920696858623e-16     -1      -0.00000000000000016                                                                                          
20  8.220635246624331e-18     -1                                                                                                        
21  4.110317623312165e-19      1       0.00000000000000000                                                                                          
22  1.957294106339126e-20      1                                                                                                        
-----------------------------------------------------------
</code></pre>