taylor expanssion calculation result is wrong

Question

Zeynep Toprak 2020-11-3

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https://ww2.mathworks.cn/matlabcentral/answers/635294-taylor-expanssion-calculation-result-is-wrong

评论： Ameer Hamza 2020-11-4

function [SN] = sintaylorfunction(A, tol)
k = 0; 
error = 0 ;
sin = 0;
SN = sin; 
sinplus1 = 0;
SM = sinplus1;
  while E <= tol
       
      sin = (-1)^k * A^(2*k+1)/factorial(2*k+1);
      
      SN = SN + sin;
      
     sinplus1 = (-1)^(k+1) * A^(2*(k+1)+1)/factorial(2*(k+1)+1);
     
     SM = SM + sinplus1;
     
     error= abs( max(SM - SN));
     
  end
end

I wrote the sin function in this way. When I calculate sin(pi/2), I get sin(pi/2) = 1.5708. However, we know that sin(pi/2) = 1. Where is my mistake in my function?

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Answer 1

Ameer Hamza 2020-11-3

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编辑：Ameer Hamza 2020-11-3

在 MATLAB Online 中打开

kou are not incrementing 'k' inside the while-loop. Also, the while-condition is incorrect. Try the following code

sintaylorfunction(pi/2, 0.01)
function [SN] = sintaylorfunction(A, tol)
k = 0;
error = inf;
sin = 0;
SN = sin;
sinplus1 = 0;
SM = sinplus1;
while error >= tol
    sin = (-1)^k * A^(2*k+1)/factorial(2*k+1);
    SN = SN + sin;
    sinplus1 = (-1)^(k+1) * A^(2*(k+1)+1)/factorial(2*(k+1)+1);
    SM = SM + sinplus1;
    error= abs( max(SM - SN));
    k = k+1;
end
end

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Zeynep Toprak 2020-11-4

many thanks dear Hamza. I see my missings.

Ameer Hamza 2020-11-4

I am glad to be of help!

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Answer 2

Steven Lord 2020-11-3

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https://ww2.mathworks.cn/matlabcentral/answers/635294-taylor-expanssion-calculation-result-is-wrong#answer_533029

编辑：Steven Lord 2020-11-3

在 MATLAB Online 中打开

I want to walk through your code and comment on a few places.

function [SN] = sintaylorfunction(A, tol)
k = 0; 
error = 0 ;

Don't create a variable named error. That identifier already has a meaning in MATLAB.

sin = 0;

The identifier sin also already has a meaning in MATLAB, so I recommend you choose a different variable name.

SN = sin; 
sinplus1 = 0;
SM = sinplus1;
  while E <= tol

The variable E doesn't exist.

sin = (-1)^k * A^(2*k+1)/factorial(2*k+1);

From the role this plays, a better name might be term.

      
      SN = SN + sin;
      
     sinplus1 = (-1)^(k+1) * A^(2*(k+1)+1)/factorial(2*(k+1)+1);
     
     SM = SM + sinplus1;
     
     error= abs( max(SM - SN));