While loop to calculate sine

I have written this code that settles on an incorrect value and I can't see what's wrong. Can anyone show me?

x = pi/4;

analytical = sin(pi/4);

k = 1;

n = 2;

es = .5^(2-n);

et(1) = 1;

sumterms(1) = 0;

while et>=es

      thisterm = (-1)^(k+1)*x^(k*2-1)/factorial(k*2-1);

      sumterms(k+1) = thisterm + sumterms(k);

      et(k+1) = abs(analytical-sumterms(k))/analytical*100;

      k = k+1;

end

I don't want to abuse the 'Ask' feature of this site so let me know if I'm asking too many questions. The answers are helpful to me if as long as I'm not taking advantage. Thank you!

Answer 1

[the cyclist]

I don't understand the significance of

es = .5^(2-n);

but that is a very lax accuracy criterion. es = 1 in your case, so you only have to calculate sin(pi/4) within 1!

I hard-coded

es = 0.0001;

and got a much more accurate value of sin(pi/4).