Calculate sin(11pi/12).

We'll write 11pi/12 = 12pi/12 - pi/12 = pi - pi/12

The angle (pi - pi/12) belongs to the second quadrant, so the sine function in the second qudrant, has positive values.

So, sin (pi - pi/12) = sin pi/12

We'll consider sin pi/12 = sin[(pi/6)/2]

But sin x/2 = sqrt[(1-cosx)/2]

sin[(pi/6)/2] = sqrt {[1-(cos pi/6)]/2}

cos pi/6 = sqrt3/2

sin[(pi/6)/2] = sqrt [(1 - sqrt3/2)/2]

sin[(pi/6)/2] = sqrt(2-sqrt3)/2