Answer
The period is $1$
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 $2\pi$, so the period is $\frac{2\pi}{2\pi}=1$