Answer
$\sqrt 2$
Work Step by Step
$\sec{\alpha} =\sec{\left( \alpha -2\pi k\right)}
\\\Rightarrow \sec{\dfrac {17\pi }{4}}=\sec{\left( \dfrac {17\pi }{4}-4\pi \right)}
\\=\sec{\dfrac {\pi }{4}}
\\=\dfrac {1}{\cos \frac {\pi }{4}}
\\=\dfrac {1}{\frac {\sqrt {2}}{2}}
\\=\sqrt {2}$
