Find the exact simplified value of sin(x/2) assuming that tan(x) = -5/12 and that 90° < x < 180°

Answer 1

sin(x/2) = +/- ((1-cos x)/2)^0.5

sec(x)^2 = tan(x)^2 + 1 = 25/144 + 1 = 169/144

cos(x)^2 = 1/sec(x)^2 = 144/169

cos(x) = -12/13 (since in Quadrant II)

Plug cos x into sin(x/2) equation.