this is a half angle problem... let sinx=-1/3 with x in Quadrant III evaluate sinx/2

Question

please I need help I don't know how to solve this!!!!!!

Answer 1

x/2 is in quadrant 2. Therefore,

cos(x) = -sqrt(8)/3,

sin(x/2) = sqrt[(1/2)(1-cosx)] = sqrt[(1/2)(1+sqrt(8)/3)]