Answer
$sin\frac{x}{2}=\frac{\sqrt {6}}{6}$
$cos\frac{x}{2}=-\frac{\sqrt {30}}{6}$
$tan\frac{x}{2}=-\frac{\sqrt 5}{5}$
Work Step by Step
Given $sec(x)=\frac{3}{2}, 270^\circ\lt x\lt 360^\circ$,
we have $cos(x)=\frac{2}{3}$ and $90^\circ\lt \frac{x}{2}\lt 135^\circ$
$sin\frac{x}{2}=\sqrt {\frac{1-cos(x)}{2}}=\frac{\sqrt {6}}{6}$
$cos\frac{x}{2}=-\sqrt {\frac{1+cos(x)}{2}}=-\frac{\sqrt {30}}{6}$
$tan\frac{x}{2}=\frac{sin\frac{x}{2}}{cos\frac{x}{2}}=-\frac{\sqrt 5}{5}$
