Answer
$\dfrac {2\sqrt {3}}{3}$
Work Step by Step
$\sec{\alpha} =\sec{\left( \alpha -2\pi n\right)}
\\ \Rightarrow \sec{\dfrac {25\pi }{6}}=\sec{\left( \dfrac {25\pi }{6}-4\pi \right)}
\\ =\sec{\dfrac {\pi }{6}}
\\=\dfrac {1}{\cos \frac {\pi }{6}}
\\=\dfrac {1}{\frac {\sqrt {3}}{2}}
\\=\dfrac {2\sqrt {3}}{3}$
