Answer
$-1$
Work Step by Step
$\sec{(\theta+ 360^{\circ} k)} = \sec{\theta}$
$\therefore \sec{540^{\circ}} = \sec{(180^{\circ}+360^{\circ})} = \sec{180^{\circ}}$
$\sec{180^{\circ}} = \dfrac{1}{\cos{a80^{\circ}}} = \dfrac{1}{-1}=\boxed{-1}$