In [1]:

    

%matplotlib notebook
import matplotlib.pyplot as plt
import math
from decimal import Decimal

def cosAprox(noIteraciones):
    x = 3
    aprox = 0
    signo = [1,-1,-1,1]
    data = []
    for iter in range(1,51):
        acum = 0
        for i in range(iter):
            if acum > 3:
                acum = 0
            aprox += Decimal(signo[acum]*(((1/(math.sqrt(2)))*(math.pow(x-(math.pi/4),i)))/(math.factorial(i))))
            #print 'Iteracion ',i,' :',aprox
            acum += 1
        print ('Resultado ',iter,' : ',format(aprox,'.32f'))
        data.append(aprox) 
        aprox=0
    print ('Resultado exacto   : ',format(math.cos(3),'.32f'))
cosAprox(20)


    

    




('Resultado ', 1, ' : ', '0.70710678118654746171500846690000')
('Resultado ', 2, ' : ', '-0.85885319510329916070645595020000')
('Resultado ', 3, ' : ', '-2.59284211487209059754377449300000')
('Resultado ', 4, ' : ', '-1.31281043274927733399692897400000')
('Resultado ', 5, ' : ', '-0.60412030421461826446005716240000')
('Resultado ', 6, ' : ', '-0.91801359626160916604931117070000')
('Resultado ', 7, ' : ', '-1.03387170643902367994648727800000')
('Resultado ', 8, ' : ', '-0.99721748021270897183176984470000')
('Resultado ', 9, ' : ', '-0.98707066562270372352128067260000')
('Resultado ', 10, ' : ', '-0.98956746053678052224555905580000')
('Resultado ', 11, ' : ', '-0.99012040119701396115835245800000')
('Resultado ', 12, ' : ', '-0.99000907906958803376149067710000')
('Resultado ', 13, ' : ', '-0.98998853455393370358739862970000')
('Resultado ', 14, ' : ', '-0.98999203439409525662434795560000')
('Resultado ', 15, ' : ', '-0.98999258801927022739062920020000')
('Resultado ', 16, ' : ', '-0.98999250628198160874611520330000')
('Resultado ', 17, ' : ', '-0.98999249496850976538592625370000')
('Resultado ', 18, ' : ', '-0.98999249644232361965985152340000')
('Resultado ', 19, ' : ', '-0.98999249662365200124236932470000')
('Resultado ', 20, ' : ', '-0.98999249660251672930127394320000')
('Resultado ', 21, ' : ', '-0.98999249660017641869838173280000')
('Resultado ', 22, ' : ', '-0.98999249660042322137263818590000')
('Resultado ', 23, ' : ', '-0.98999249660044806544789667510000')
('Resultado ', 24, ' : ', '-0.98999249660044567328551858200000')
('Resultado ', 25, ' : ', '-0.98999249660044545254855208300000')
('Resultado ', 26, ' : ', '-0.98999249660044547210233173960000')
('Resultado ', 27, ' : ', '-0.98999249660044547376786390650000')
('Resultado ', 28, ' : ', '-0.98999249660044547363125314370000')
('Resultado ', 29, ' : ', '-0.98999249660044547362044819920000')
('Resultado ', 30, ' : ', '-0.98999249660044547362127332510000')
('Resultado ', 31, ' : ', '-0.98999249660044547362133423590000')
('Resultado ', 32, ' : ', '-0.98999249660044547362132988450000')
('Resultado ', 33, ' : ', '-0.98999249660044547362132958340000')
('Resultado ', 34, ' : ', '-0.98999249660044547362132960360000')
('Resultado ', 35, ' : ', '-0.98999249660044547362132960490000')
('Resultado ', 36, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 37, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 38, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 39, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 40, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 41, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 42, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 43, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 44, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 45, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 46, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 47, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 48, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 49, ' : ', '-0.98999249660044547362132960480000')
('Resultado ', 50, ' : ', '-0.98999249660044547362132960480000')
('Resultado exacto   : ', '-0.98999249660044541521131122863153')