MATLAB: Taylor expanssion calculation result is wrong

cossintaylorwhile loop

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?

Best Answer

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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