Answer
\[\frac{{\sqrt 3 }}{2}\]
Work Step by Step
$$\eqalign{
& \sin \frac{\pi }{3} \cr
& {\text{convert }}\frac{\pi }{3}{\text{radians to degrees}} \cr
& \frac{\pi }{3}{\text{radians}} = \frac{\pi }{3}\left( {\frac{{{{180}^ \circ }}}{\pi }} \right) \cr
& \frac{\pi }{3}{\text{radians}} = {60^ \circ } \cr
& \sin \frac{\pi }{3} = \sin {60^ \circ } \cr
& {\text{using the }}{30^ \circ }{\text{ - 6}}{{\text{0}}^ \circ }{\text{ - 9}}{{\text{0}}^ \circ }{\text{ triangle to obtain}} \cr
& \sin {30^ \circ } = \frac{y}{r} = \frac{{\sqrt 3 }}{2} \cr
& {\text{then }} \cr
& \sin \frac{\pi }{3} = \frac{{\sqrt 3 }}{2} \cr} $$
