# What is the exact value of sec-330

What is the exact value of $\mathrm{sec}-330$?
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$\mathrm{sec}\left(-330\right)$
-330 will be in the first quadrant
-330=+30
$\therefore \mathrm{sec}\left(-330\right)=\mathrm{sec}30$
$\mathrm{sec}30=\frac{1}{\mathrm{cos}30}$
$\because \mathrm{cos}30=\frac{\sqrt{3}}{2}$
$\mathrm{sec}30=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}$
rationalising
$\mathrm{sec}30=\frac{2\sqrt{3}}{3}$