Question

if cos x=2/3 and x is in quadrant 4 find tan(x/2),sin(x/2),and cos(x/2)
i got
sin(x/2)=squr 1/6
tan(x/2)=squr 2/6
cos(x/2)=squr 5/6

Answer 1

I mentally draw the triangle
adjacent x:2
hypotenuse:3
opposite: -sqrt5
Half angle formlas:
sin(x/2)=+- sqrt((1-cosx)/2)
it is in the 4th quad, so neg sign applies
sin(x/2)=- sqrt(1/6)
see http://www.freemathhelp.com/images/halfangles.png for the other formulas (or see your text)