Answer
$sin\frac{x}{2}=\frac{\sqrt {10}}{10}$,
$cos\frac{x}{2}=\frac{3\sqrt {10}}{10}$,
$tan\frac{x}{2}=\frac{1}{3}$
Work Step by Step
Given $sin(x)=\frac{3}{5}$ and $0^\circ\lt x\lt 90^\circ$, we have $0^\circ\lt x/2\lt 45^\circ$ and
$cos(x)=\sqrt {1-sin^2x}=\frac{4}{5}$. thus $sin\frac{x}{2}=\sqrt {\frac{1-cos(x)}{2}}=\frac{\sqrt {10}}{10}$. $cos\frac{x}{2}=\sqrt {\frac{1+cos(x)}{2}}=\frac{3\sqrt {10}}{10}$ and $tan\frac{x}{2}=\frac{sin\frac{x}{2}}{cos\frac{x}{2}}=\frac{1}{3}$
