Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 596: 58

Please see below.

Please note that the graph of the function $y=2\cos \frac{1}{2}x +1$ (the red graph) is the graph of the function $y=2\cos \frac{1}{2}x$ (the blue graph) shifted up one unit. The period of the graph is $\frac{2\pi }{\frac{1}{2}}=4\pi$.