Use a half-angle formula to find sin(11π/12).

Answer 1

sin(11π/12) = sin(π/12) = √(1 - cos(π/6))/2 = √(2 - √3)/2

Answer 2

half angle formula for sines is

sin(x/2) = + or - sqr((1-cosx)/2)

sin(11pi/12 )= + or - sqr((1-cos11pi/6)/2) 11pi/6 = -30 degrees cos-30=sqr3/2=1.732/2=.866

= + or - sqr((1-.866)/2) = + or - sqr(.134/2) =

= + or - sqr((1-(sqr3/2))/2) = + sqr(1/2-sqr3)/4 = .259 11pi/12 is in 2nd quadrant where sines >0

11pi/12 = 165 degrees, sin165 = about .259