python - calculate cos(x) by summing a series -

i'm new in computer programming , started on learning python. in assignment need calculate cos(x) summing series 1 - x^2/2! + x^4/4! - x^6/6! . . .

how do without using numpy or m.factorial? think i'm supposed use while loop. here code far

print("investigation of complex infinite series") print("") print("part a: exp, cos , sin series 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 far total = 0.0 # total of terms far termsign = 1  term = 1.0 # initial term xx = 1  while abs(term) > 1e-20:     count += 1     print("%2d   %22.16g    %2d" % (count, term, termsign))     termsign = (-1)**(count//2)     total = total + term     term = term/count 

the output of code should this:

 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                                                                                                         ----------------------------------------------------------- 

you're close ... left out couple of computation steps.

x = 3.1415926535 / 4  sum_up = 1 term = 1 converge = 1e-20 = 1 while abs(term) > converge:     term = -term * x * x / (i * (i+1))     sum_up += term     += 2  print sum_up 

output:

0.707106781202