find the value for sin (x/2) if the following conditions hold: cos(x) =-1/3 and x is in quadrant 2

Question

find the value for sin (x/2) if the following conditions hold: cos(x) =-1/3 and x is in quadrant 2

Answer 1

If x in quadrant 2 then x/2 is in quadrant 1.

sinx/2 = sqrt((1-cox)/2) = sqrt((1+1/3)/2) = sqrt(2/3) =(sqrt6)/3