Answer
$-1$
Work Step by Step
Recall: $ \sec \pi =\dfrac{1}{\cos \pi}$
We need to compute $\sec (- \pi)$.
The trigonometric function $\cos$ and its inverse trigonometric function $\sec x$ has a period of $2\pi$. Also, because cosine and secant is even so we can write $\cos (-x)=\cos (x)$ and $\sec (- \pi) = \sec \pi$
Thus, we can simplify as follows:
$\sec (- \pi) = \sec \pi =\dfrac{1}{\cos \pi}\\=\dfrac{1}{-1} \\ =-1$