This is done through the use of the unit circle.
Your first step is to convert the angle 11π / 2 to an angle between 0 and 2π, which is the range of angles on the unit circle.
This can be done by splitting the circle into sections of π / 2 and counting up 11 sections, or by simply recognizing the fact that 12π / 2 is the same as 6π, which is also the same as 2π. Therefore, we can conclude that 11π / 2 (π / 2 less) is the same angle as 3π / 2.
So we are really finding sin (3π / 2), which is -1 (the y-value of the coordinate at the angle 3π / 2).