Recall that the following Taylor series is used to approximate Cosine: (-1)x2n cos(x) = (2n)! n=0...

 

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Recall that the following Taylor series is used to approximate Cosine: (-1)"x2n cos(x) = (2n)! n=0 You have been tasked with developing an M-file that allows other engineers to quickly determine the minimum n needed to reduce the truncation error below an error threshold. The truncation error is the absolute error between the approximation and MATLAB's cos() function. Note: You may want to Google the Taylor series to gain a better understanding of it. Your code should do the following: 1. Ask the user to enter an error threshold value (it should work with vectors) 2. Find the number of terms (minimum n) needed so that the truncation error is below the user error threshold for x = -2n to 2n. 3. Print the minimum n value, the mean truncation error and the maximum truncation error using fprintf. 4. Plot the truncation error against x. Test your code with the following error thresholds: 0.1, 0.01, le-10. The answers for the thresholds above should be n=8, 9, 16, respectively. This is a reference to see whether your code is working correctly. Hint: Your code may include both while and for loops and/or a created function to calculate the approximation of Cosine. Recall that the following Taylor series is used to approximate Cosine: (-1)"x2n cos(x) = (2n)! n=0 You have been tasked with developing an M-file that allows other engineers to quickly determine the minimum n needed to reduce the truncation error below an error threshold. The truncation error is the absolute error between the approximation and MATLAB's cos() function. Note: You may want to Google the Taylor series to gain a better understanding of it. Your code should do the following: 1. Ask the user to enter an error threshold value (it should work with vectors) 2. Find the number of terms (minimum n) needed so that the truncation error is below the user error threshold for x = -2n to 2n. 3. Print the minimum n value, the mean truncation error and the maximum truncation error using fprintf. 4. Plot the truncation error against x. Test your code with the following error thresholds: 0.1, 0.01, le-10. The answers for the thresholds above should be n=8, 9, 16, respectively. This is a reference to see whether your code is working correctly. Hint: Your code may include both while and for loops and/or a created function to calculate the approximation of Cosine.

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