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Text: MATLAB programming with repetition structures The cosine function can be evaluated by the following infinite series, where x is in radians: cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + ... Here, the 2k factorial, (2k)! = 1 * 2 * 3 * ... * 2k, can be computed with MATLAB's function factorial(). For example, 6! = 1 * 2 * 3 * 4 * 5 * 6 is computed with "factorial(6)" in MATLAB. Step 1: Create an M-file with a repetition (i.e., for-loop) structure based on the incomplete sample code below to compute and display the value of cos(x) as terms are added in its series up to a maximum number of terms. Specifically, compute and display values for each of these truncated series: cos(x) = 1 for k = 0 (giving k + 1 = 1 term), cos(x) = 1 - (x^2/2!) for k = 1 (giving k + 1 = 2 terms), cos(x) = 1 - (x^2/2!) + (x^4/4!) for k = 2 (giving k + 1 = 3 terms), cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) for k = 3 (giving k + 1 = 4 terms), ... up to a user-defined maximum number of terms. For each number of terms, compute and display the absolute value of the true relative error, Îµt, as defined by: Îµt = 100% * (true value - approximation) / true value Step 3: For nine terms in the series, i.e., k = 8, test the M-file with the data in the following table while stating the missing values for cos(x) and the percent error: x | cos(x) | Error% 0.2 | 0.9801 | 0 0.7 | | 1.25 | | clc; clear all; x = input('Enter the value of x in radians: '); cos_x = 0; for k = 0:8 disp(['With ', num2str(k+1), ' terms, we have ']) true_relative_error = ? end

          Text: MATLAB programming with repetition structures
The cosine function can be evaluated by the following infinite series, where x is in radians:
cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + ...
Here, the 2k factorial, (2k)! = 1 * 2 * 3 * ... * 2k, can be computed with MATLAB's function factorial(). For example, 6! = 1 * 2 * 3 * 4 * 5 * 6 is computed with "factorial(6)" in MATLAB.
Step 1: Create an M-file with a repetition (i.e., for-loop) structure based on the incomplete sample code below to compute and display the value of cos(x) as terms are added in its series up to a maximum number of terms. Specifically, compute and display values for each of these truncated series:
cos(x) = 1 for k = 0 (giving k + 1 = 1 term),
cos(x) = 1 - (x^2/2!) for k = 1 (giving k + 1 = 2 terms),
cos(x) = 1 - (x^2/2!) + (x^4/4!) for k = 2 (giving k + 1 = 3 terms),
cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) for k = 3 (giving k + 1 = 4 terms),
...
up to a user-defined maximum number of terms. For each number of terms, compute and display the absolute value of the true relative error, Îµt, as defined by:
Îµt = 100% * (true value - approximation) / true value
Step 3: For nine terms in the series, i.e., k = 8, test the M-file with the data in the following table while stating the missing values for cos(x) and the percent error:
x     | cos(x) | Error%
0.2   | 0.9801 | 0
0.7   |        | 
1.25  |        | 

clc; clear all;
x = input('Enter the value of x in radians: ');
cos_x = 0;
for k = 0:8
    disp(['With ', num2str(k+1), ' terms, we have '])
    true_relative_error = ? 
end

matlab programming with repetition structures the cosine function can be evaluated by the following infinite series where x is in radians x2x3x6 2k246 k0 here the 2k factorial 2k 1 2 3 2k ca 38344

Added by Emilia J.

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