(i) \[tan\text{ }7\pi /4\] 

\[tan\text{ }7\pi /4\text{ }=\text{ }tan\text{ }{{315}^{o}}\]

\[=\text{ }tan\text{ }{{\left( 90\times 3\text{ }+\text{ }45 \right)}^{o}}\]

Since,\[{{315}^{o}}\] lies in the \[IV\text{ }quadrant\] in which tangent function is negative.

\[tan\text{ }{{315}^{o}}~=\text{ }tan\text{ }{{\left( 90\times 3\text{ }+\text{ }45 \right)}^{o}}\]

\[=\text{ }-\text{ }cot\text{ }{{45}^{o}}\]

\[=\text{ }-1\]

(ii) \[sin\text{ }17\pi /6\]

\[sin\text{ }17\pi /6\text{ }=\text{ }sin\text{ }{{510}^{o}}\]

\[=\text{ }sin\text{ }{{\left( 90\times 5\text{ }+\text{ }60 \right)}^{o}}\]

Since,\[{{510}^{o}}\] lies in the \[II\text{ }quadrant\]in which sine function is positive.

\[sin\text{ }{{510}^{o}}~=\text{ }sin\text{ }{{\left( 90\times 5\text{ }+\text{ }60 \right)}^{o}}\]

\[=\text{ }cos\text{ }{{60}^{o}}\]

\[=\text{ }1/2\]