Good question.
Here is one way of thinking about it.
You see that -11/6 is very close to -12/6 which would be equal to -2, so I would first try to rewrite as such:
(-11pi)/6 = (-12pi)/6 + pi/6 = -2pi + pi/6
You are asked to compute the sine and cosine of that angle, so this can be written:
cos((-11pi)/6) = cos(-2pi +pi/6)
and
sin((-11pi)/6) = sin(-2pi +pi/6)
Now, picture yourself the trigonometric circle.
Going around a full circle is 2 pi (radian), so if you add 2pi, or any multiple of 2pi if you're going full-circle many times, to whatever angle, you come back to where you started from (of course, it's the same thing if you subtract 2pi!).
So,
cos(-2pi + pi/6) = cos(pi/6)
and
sin(-2pi + pi/6) = sin(pi/6)
and these are equal to
cos(pi/6)=sqrt(3)/2
and
sin(pi/6)=1/2.
I hope this helps.
