Question

In MATLAB

The value of cos(x) can be approximated using a Maclaurin series + +... cos(x)=1-1 2! 4! 6! Which can be expressed compactly as cos(x) = {(-1)+7 (2(k-1))! 00 2(k-1) k-1 Write Matlab code using a while loop that calculates cos(2) with 5 terms of Maclaurin series. Compare the value with the one calculated with a built-in function cos (2) in Matlab. The following is an expected output from your code: Using the Maclaurin series cos( 2.0) with 5 terms is -0.4159 The value of cos(x) using the built-in cos function is -0.4161

Answer 1

clc;
clear;
close all;
x = 2;
k = 1;
sum = 0;
while (k <= 5)
sum = sum + (-1)^(k-1)*(x^(2*(k-1)))/factorial(2*(k-1));
k = k+1;
end
val = cos(2);
fprintf('Using the Maclaurin series cos(2.0) with 5 terms is %0.4f \n',sum);
fprintf('The value of cos(x) using the built-in cos function is %0.4f \n',val);

Find Files Run Section Compare Go To Insert fx Fil Comment % 9 % Indent 5 New Open Save Breakpoints Run Advance Run and Advance Run and Time Print Find FILE NAVIGATE EDIT BREAKPOINTS RUN + m 1 - N cos_sum.m clc; clear; 3 close all; 4 - x = 2; 5 - k = 1; 6 sum = 0; 7 - while (k <= 5) sum = sum + (-1)^(k-1)*(x^(2* (k-1)))/factorial (2* (k-1)); k = k+1; 10 end 11 - val - cos (2); 12 - fprintf('Using the Maclaurin series cos (2.0) with 5 terms is 30.4f \n', sum); 13 - fprintf('The value of cos(x) using the built-in cos function is 30.4f \n', val); 14 0001 - 15

Command Window Using the Maclaurin series cos (2.0) with 5 terms is -0.4159 The value of cos(x) using the built-in cos function is -0.4161 fx >> |