Answer
$-1$
Work Step by Step
We know that $\sin$, $\csc$, $\tan$ are odd functions, which means $f(-\theta)=-f(\theta).$
We also know that $\cos$, $\sec$, are even functions, which means $f(-\theta)=f(\theta).$
Therefore,
$\sec{(-\pi)}=\sec{\pi}=\dfrac{1}{\cos{\pi}}=\dfrac{1}{-1}=-1$