Answer
The period is $8\pi$
Work Step by Step
To find the period, one must first find $b$ in the base equation of secant functions $f(x)=a\cdot $sec$(b(x-c))+d$, then use $\frac{2\pi}{b}$. In this case, $b$ is $1/4$, so the period is $\frac{2\pi}{1/4}=8\pi$
