Question

Convince yourself that the Maclaurin Series for cos(x) is:

2k (2k)! k-0 (N-term approximation)

A. Write a function script called cos_series that takes that takes as its inputs, x and N and has output given by the sum in the N-term Maclaurin Series approximation for Cos(x). Hint: try a “for loop” and set “format long” in your code. You may use the MATLAB built-in function factorial()

B. Check your code by finding the 2-terms, 3-terms, 4-terms, 5-terms and 6-terms Maclaurin Series approximations every 30 degrees for Cos(x) where 0<x<360. Display a Table using fprintf() display a Table with thirteen rows (0, 30, 60, 90, . . . . . ., 360) and five columns (x in Degrees, 2,3,4,5, and 6-term computations) for comparison.

You MUST NOT use the MATLAB built-in function, table()

Answer 1

%%%%%%%%%%%%%%%%%%%%%%%% Part A

function Cos_x=cos_series(x,N)
format long
s = 0;
for k = 0: N % need more code here

s =s+(-1)^k*(x^(2*k)/factorial(2*k));

end
Cos_x=s;

%%%%%%%%%%%%%%%%%%%%%%%% Part B

clc;
clear all;
n=0:30:360;
for i=1:13
x(i)=n(i)*pi/180;
end
disp(' x in deg 2-terms 3-terms 4-terms 5-terms 6-terms')
disp('_______________________________________________________________________________________________')
for i=1:13
fprintf('%f \t %10f \t %10f \t %10f \t %10f \t %10f\n \n',n(i),cos_series(x(i),2),cos_series(x(i),3),cos_series(x(i),4),cos_series(x(i),5),cos_series(x(i),6))
end

%%%%%% Solution

x in deg 2-terms 3-terms 4-terms 5-terms 6-terms
_______________________________________________________________________________________________
0.000000    1.000000    1.000000    1.000000    1.000000    1.000000

30.000000    0.866054    0.866025    0.866025    0.866025    0.866025

60.000000    0.501796    0.499965    0.500000    0.500000    0.500000

90.000000    0.019969    -0.000895    0.000025    -0.000000    0.000000

120.000000    -0.391525    -0.508749    -0.499567    -0.500015    -0.500000

150.000000    -0.469620    -0.916796    -0.862066    -0.866234    -0.866017

180.000000    0.123910    -1.211353    -0.976022    -1.001829    -0.999900

210.000000    1.802451    -1.564583    -0.756878    -0.877438    -0.865168

240.000000    5.054553    -2.447829    -0.097177    -0.555448    -0.494533

270.000000    10.443925    -4.765552    1.265714    -0.222441    0.027914

300.000000    18.609439    -10.009876    4.001102    -0.266886    0.619548

330.000000    30.265128    -20.435735    9.598041    -1.472020    1.309990

360.000000    46.200185    -39.256632    20.988009    -5.438247    2.465289

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