Chapter 4 - Section 4.6 - Graphs of Other Trigonometric Functions - Exercise Set - Page 610: 36

Please see below.

Please note that since $\sec (Bx-C)=\frac{1}{\cos (Bx-C)}$, the period of the secant function is the same as the period of the cosine function, that is, $\frac{2\pi }{B}$. So the period of the function $y=\sec \frac{x}{2}$ is $\frac{2\pi }{\frac{1}{2} }=4\pi$.