Answer
$\dfrac {\sqrt {2}}{2}$
Work Step by Step
$\cos \alpha =\cos \left( \alpha -2\pi k\right)
\\\Rightarrow \cos \dfrac {33\pi }{4}=\cos \left( \dfrac {33\pi }{4}-8\pi \right)
\\=\cos \dfrac {\pi }{4}
\\=\dfrac {\sqrt {2}}{2}$
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