How can I obtain the right convergence number from what I have done so far??

Hello Everybody, I hope you are doing well.

I was asked to write a script which calculates the number of terms or iterations needed for a taylor series approximation of cos(x) to converge using a while.

The condition requires that the loop should continue as long as abs(Estimate – Previous Estimate) exceeds 0.00001.

Here is my script:

clc
clear

PreviousEstimate = inf;
x = input('Enter the angle in radians: ');
Count = 0;
Estimate = 1;

while abs(Estimate - PreviousEstimate) > 0.00001
    Estimate(Count+1) = (-1)^Count*(x.^(2*Count))/factorial(2*Count);
    Count = 0 + 1;
    PreviousEstimate = Estimate;
end
fprintf('%i terms required for convergence. \n',Count)

Answer 1

[Mathieu NOE]

hello

this seems to work better - :)

clc
clear
x = input('Enter the angle in radians: ');
Count = 0;
Estimate = inf;
PreviousEstimate = 0;

while abs(Estimate - PreviousEstimate) > 1e-6
    PreviousEstimate = Estimate;
    Estimate = (-1)^Count*(x.^(2*Count))/factorial(2*Count);
    Count = Count + 1;
    
end
fprintf('%i terms required for convergence. \n',Count)

[Edivaldo Bartolomeu]

Hi Mathieu,

Thanks for replying.

However, I am still getting this answer "1 terms required for convergence." for every angle I introduce.

[Mathieu NOE]

hello

funny because on my side I got these results - I also checked that the sum of the series terms are actually matching with "true" cos value :

Enter the angle in radians: 1

7 terms required for convergence.

Enter the angle in radians: 2

9 terms required for convergence.

Enter the angle in radians: 3

11 terms required for convergence.

Enter the angle in radians: 4

12 terms required for convergence.

Enter the angle in radians: 5

14 terms required for convergence.

Enter the angle in radians: 6

15 terms required for convergence.

Again, this is the code used to generate the above results :

clc
clear
x = input('Enter the angle in radians: ');
Count = 0;
Estimate = inf;
PreviousEstimate = 0;

while abs(Estimate - PreviousEstimate) > 1e-6
    PreviousEstimate = Estimate;
    Estimate = (-1)^Count*(x.^(2*Count))/factorial(2*Count);
    Count = Count + 1;
    
end
fprintf('%i terms required for convergence. \n',Count)

[Edivaldo Bartolomeu]

My bad Mathieu you are absolutely right, I made a mistake in the first attempts.

Thanks for your help.

[Mathieu NOE]

ok ! good luck for the future !