(i) \[tan\text{ }11\pi /6\]

\[tan\text{ }11\pi /6\text{ }=\text{ }{{\left( 11/6\text{ }\times \text{ }180 \right)}^{o}}\]

\[=\text{ }{{330}^{o}}\]

Since,\[{{330}^{o}}\] lies in the \[IV\text{ }quadrant\]in which tangent function is negative.

\[tan\text{ }11\pi /6\text{ }=\text{ }tan\text{ }{{\left( 300 \right)}^{o}}\]

\[=\text{ }tan\text{ }{{\left( 90\times 3\text{ }+\text{ }60 \right)}^{o}}\]

Or,

\[=\text{ }-\text{ }cot\text{ }{{60}^{o}}\]

\[=\text{ }-\text{ }1/\surd 3\]

(ii) \[cos\text{ }\left( -25\pi /4 \right)\]

\[cos\text{ }\left( -25\pi /4 \right)\text{ }=\text{ }cos\text{ }{{\left( -1125 \right)}^{o}}\]

\[=\text{ }cos\text{ }{{\left( 1125 \right)}^{o}}\]

Since,\[{{1125}^{o}}\] lies in the \[I\text{ }quadrant\]in which cosine function is positive.

\[cos\text{ }{{\left( 1125 \right)}^{o}}~\]

\[=\text{ }cos\text{ }{{\left( 90\times 12\text{ }+\text{ }45 \right)}^{o}}\]

Or,

\[=\text{ }cos\text{ }{{45}^{o}}\]

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