Trig
posted by Lauren .
cos(11pi/12)

sometimes I find it easier to visualize these kind of angles in degrees
π/12 radians = 15°,
so 11π/12 = 165°
and 165 = 120+45
cos(11π/12) = cos(165° = cos(165°)
= cos(120 + 45)
= cos120cos45  sin120sin45
= (1/2)(1/√2)  (√3/2)(1/√2)
= (1  √3)/(2√2)
or
= (√2  √6)/4