## Algebra 2 (1st Edition)

$\dfrac{2 \sqrt 5}{5}$
Need to divide the interval by $2$: Thus, we have $\dfrac{\pi}{4} \lt \dfrac{a}{2} \lt \dfrac{\pi}{2}$ Since $\sin a$ is positive in the First quadrant. That is, $\sin \dfrac{a}{2} \gt 0$ Thus, $\sin \dfrac{a}{2}= \sqrt {\dfrac{1- \cos a}{2}}= \sqrt {\dfrac{1+(3/5)}{2}}$ $\sin \dfrac{a}{2} =\sqrt {\dfrac{4}{5}}=\dfrac{2 \sqrt 5}{5}$