Answer
-1
Work Step by Step
We can find the secant of coterminal angle that lies between $0^{\circ}$ and $360^{\circ}$ for convenience.
$\sec(-540^{\circ})= \sec(-540^{\circ}+2\cdot360^{\circ})=\sec 180^{\circ}$
The terminal side of $180^{\circ}$ angle passes through (-1,0). So $x=-1,y=0$ and $r=1$.
$\sec 180^{\circ}=\frac{r}{x}=\frac{1}{-1}=-1$
