(i) \[sin\text{ }5\pi /3\]

\[5\pi /3\text{ }=\text{ }{{\left( 5\pi /3\text{ }\times \text{ }180 \right)}^{o}}\]

\[=\text{ }{{300}^{o}}\]

Or,

\[=\text{ }{{\left( 90\times 3\text{ }+\text{ }30 \right)}^{o}}\]

Since, \[{{300}^{o}}~lies\text{ }in\text{ }IV\text{ }quadrant\] in which sine function is negative.

\[sin\text{ }5\pi /3\text{ }=\text{ }sin\text{ }{{\left( 300 \right)}^{o}}\]

\[=\text{ }sin\text{ }{{\left( 90\times 3\text{ }+\text{ }30 \right)}^{o}}\]

\[=\text{ }-\text{ }cos\text{ }{{30}^{o}}\]

So,

\[=\text{ }-\text{ }\surd 3/2\]

 (ii) \[sin\text{ }17\pi \]

\[Sin\text{ }17\pi \text{ }=\text{ }sin\text{ }{{3060}^{o}}\]

\[=\text{ }sin\text{ }{{\left( 90\times 34\text{ }+\text{ }0 \right)}^{o}}\]

Since,\[{{3060}^{o}}\] lies in the negative direction of \[x-axis\]i.e., on boundary line of \[II\text{ }and\text{ }III\text{ }quadrants\]

\[Sin\text{ }17\pi \text{ }=\text{ }sin\text{ }{{\left( 90\times 34\text{ }+\text{ }0 \right)}^{o}}\]

\[=\text{ }-\text{ }sin\text{ }{{0}^{o}}\]

\[=\text{ }0\]