Write a regular function (i.e. in a function .m file) to calculate the series expansion of cosine(x). The number of terms calculated in the series should be specified in the input list of the function. Write a separate function that determines when the series expansion begins to deviate by at least 10% from the true value of cosine(x) based on the number of terms calculated in the series expansion, n. For n = 1, 2, … 10, determine the values of x where deviation between cosine(x) and the series expansion occur. Display the values in a MATLAB® Table. Create a single, properly-formatted plot that visually shows your results are correct.
If you have any clarification needed please ask. If you need any extra plots or results needed on the same please do ask.
Main code
clc;
clear;
x=[-179:1:180]*(pi/180); %(deg to rad conversion)
for i=1:length(x)
for j=1:10
c = cos_series(x(i),j);
[t,er] = cos_series_dev(x(i),j);
if t==1
r(:,i)=[(180/pi)*x(i),j,er];
j=1;
end
end
end
[ind]= find(r(1,:)==0)
r(:,ind)=[];
angle_in_deg=r(1,:);
number_of_terms=r(2,:);
table(angle_in_deg',number_of_terms')
stem(r(1,:),r(3,:));
ylable('Error');
xlable('Angle');
__________________________________________________________________________________________________
Functions
__________________________________________________________________________________________________
function [c] = cos_series( x,n )
%Computes series epantion of cos(x)
%v: The x value
%n: Number of terms in the expansion
c=0;
for i=1:length(x)
for k=0:n
term_k=((-1)^k)*(x^(2*k))/(factorial(2*k));
c=c+term_k;
end
end
end
--------------------------------------------------------------------------------------------------------------------------------------------------
function [t,deviation] = cos_series_dev( x,n )
%Computes deviation of cos(x) values
%v: The x value
%n: Number of terms in the expansion
d=sum(abs(cos(x)-cos_series(x,n)));
deviation=abs((d/cos(x))*100);
if deviation>=10
% disp('The series expansion deviates from the actual
value');
t=1;
else
t=0;
end
end
______________________________________________________________________
Results
Var1-angle, var2:Min number of terms to have err<10
Var1 Var2
____ ____
-179 3
-178 3
-177 3
-176 3
-175 3
-174 3
-173 3
-172 3
-171 3
-170 3
-169 3
-168 3
-167 3
-166 3
-165 3
-164 3
-163 3
-162 2
-161 2
-160 2
-159 2
-158 2
-157 2
-156 2
-155 2
-154 2
-153 2
-152 2
-151 2
-150 2
-149 2
-148 2
-147 2
-146 2
-145 2
-144 2
-143 2
-142 2
-141 2
-140 2
-139 2
-138 2
-137 2
-136 2
-135 2
-134 2
-133 2
-132 2
-131 2
-130 2
-129 2
-128 2
-127 2
-126 2
-125 2
-124 2
-123 2
-122 2
-121 2
-120 2
-119 2
-118 2
-117 2
-116 2
-115 2
-114 2
-113 2
-112 2
-111 2
-110 2
-109 2
-108 2
-107 2
-106 2
-105 2
-104 2
-103 2
-102 2
-101 2
-100 2
-99 2
-98 2
-97 2
-96 2
-95 2
-94 2
-93 2
-92 2
-91 2
-90 9
-89 2
-88 2
-87 2
-86 2
-85 2
-84 2
-83 2
-82 1
-81 1
-80 1
-79 1
-78 1
-77 1
-76 1
-75 1
-74 1
-73 1
-72 1
-71 1
-70 1
-69 1
-68 1
-67 1
-66 1
-65 1
-64 1
-63 1
-62 1
-61 1
61 1
62 1
63 1
64 1
65 1
66 1
67 1
68 1
69 1
70 1
71 1
72 1
73 1
74 1
75 1
76 1
77 1
78 1
79 1
80 1
81 1
82 1
83 2
84 2
85 2
86 2
87 2
88 2
89 2
90 9
91 2
92 2
93 2
94 2
95 2
96 2
97 2
98 2
99 2
100 2
101 2
102 2
103 2
104 2
105 2
106 2
107 2
108 2
109 2
110 2
111 2
112 2
113 2
114 2
115 2
116 2
117 2
118 2
119 2
120 2
121 2
122 2
123 2
124 2
125 2
126 2
127 2
128 2
129 2
130 2
131 2
132 2
133 2
134 2
135 2
136 2
137 2
138 2
139 2
140 2
141 2
142 2
143 2
144 2
145 2
146 2
147 2
148 2
149 2
150 2
151 2
152 2
153 2
154 2
155 2
156 2
157 2
158 2
159 2
160 2
161 2
162 2
163 3
164 3
165 3
166 3
167 3
168 3
169 3
170 3
171 3
172 3
173 3
174 3
175 3
176 3
177 3
178 3
179 3
180 3
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