Use Half-angle formula: [tex]sin (\frac{x}{2}) = \sqrt{\frac{1-cos x}{2}}[/tex]
We need cos(x), which can be found using pythagorean identity: [tex]sin^2 + cos^2 = 1[/tex] Note that the angle is in 2nd quadrant indicating that cos(x) is negative. [tex]cos(x) = -\sqrt{1 - (7/9)^2} = -\sqrt{\frac{81-49}{81}} = -\frac{4 \sqrt{2}}{9}[/tex]
Substitute this value into the half-angle formula: [tex]sin(\frac{x}{2}) = \sqrt{\frac{1 - (-4\sqrt{2}/9)}{2}} = \sqrt{\frac{9+4 \sqrt{2}}{18}}[/tex]
