implementing taylor series with loop

I want to implement taylor series for sinx with loop.

So , :

angle=input('Insert angle in degrees\n');

x=angle*2*pi/360; %convert to radians because the equation is in radians
eps=0.000001;%accuracy
sumation=0;
err=1;%error
n=0;

while err>eps

      term=((((-1)^n)/factorial(2*n+1))*(x^2*n +1));
      sumation=sumation+term;
      err=abs((sumation-term)/term);
      n=n+1;
  end
  result=sumation

I think the problem is in computing the error.The error = ((sum(n)-sum(n-1))/sum(n-1)). I tried it also with sumation as a vector but still with no success.

Thanks!

Answer 1

[Image Analyst]

Is this homework? Don't compare the small latest term you are adding on (say 0.003) to the whole sum (say .707 for 45 degrees). Those are the wrong things to compare. Either compare the sum to the true value (sind(angle)) or compare your latest term to the prior term, which means you'd have to make term an array.

[George]

It's not homework.For the error you mean

 term(n+1)=((((-1)^n)/factorial(2*n+1))*(x^2*n +1));

 sumation=sumation+term(n+1);

But I can't figure how to write the error because n starts from 0.

[Image Analyst]

You could keep track of them separately.

x=angle*2*pi/360; %convert to radians because the equation is in radians
myEps=0.000001;%accuracy
summation=0;
err=1;%error
n = 0;
index = 1;
% Calculate first term.
term(index) = ((((-1)^n)/factorial(2*n+1))*(x^2*n +1));
% Calculate additional terms.
n=n+1;
index = index + 1;
while err > myEps
  term(index) = ((((-1)^n)/factorial(2*n+1))*(x^2*n +1));
  summation=summation+term(index);
  err=abs((term(index) - term(index-1))/term(index));
  n=n+1;
  index = index + 1;
end
result=summation
trueResult = sind(angle)

but I don't know if your formula is correct.

[George]

Ok, thanks now I understand!

[George]

I had one mistake : term(index) = ((((-1)^n)/factorial(2*n+1))*(x^(2*n +1))); The "x^(2*n+1)".I corrected this and also added "result=sind(sumation)" but I still don't get right results.... The formula is : http://www.wolframalpha.com/input/?i=taylor+series+sin+x...