Pre-calculus/trig

Here is a webpage .......look at   Hal Angle formulas and see what you find.

http://home.windstream.net/okrebs/page103.html

Remember   Sin and COs are both negative in Quadrant III

sin = -4/5                                     cos = - 3/5     (because cos^2 = 1- sin^2)

Then go from there ......

I'll use the first evalution to see if I get the same answer as you did:

Tan x/2 = +-  sqrt (   (1-cosx) /(1+cos x) )

              =+-sqrt (  (1- -3/5)/(1+ -3/5)  )   = + -  sqrt( 8/8  /  2/5)  = +-sqrt  (4)  =+2 or  -2       We know it is the negative one because it is in Q II

So YES!   The answer is  -2  !!!