How to make my bisection method more accurate?

I have constructed a root-finding function based on the bisection method. The function works, however, the roots it gives me aren't as accurate as I want them to be. They are off of about 1e-4 when compared to the exact roots. I don't understand how I can make it more accurate. Can someone please help. Here's my code:

function root = bisection(f,a,b,tol)
if sign(f(a))==sign(f(b))
    error('a and b do not bracket the root');
end
j = 1;
while abs(0.5*(b-a)) >= tol
    root = 0.5*(a+b);
    j = j+1;
    if sign(f(a))==sign(f(root))
        a = root;
    else
        b = root;
    end
end
end

Answer 1

[James Tursa]

Change tol to a smaller value. E.g.,

>> f = @sin
f = 
    @sin
>> a = -.1
a =
   -0.1000
>> b = .2
b =
    0.2000
>> bisection(f,a,b,1e-4)
ans =
  4.8828e-005
>> bisection(f,a,b,1e-10)
ans =
  4.6566e-011
>>