## Precalculus (6th Edition) Blitzer

$$y=\pi \cos (2\pi x + 4\pi )$$
Please note that the function $y=A \cos (Bx-C)$ represents a cosine function with amplitude $A$, period $\frac{2 \pi }{B}$, and phase shift $\frac{C}{B}$. So, according to the information given in the question, we have$$A= \pi, \quad B=\frac{2\pi }{1}=2\pi, \quad C=(2\pi )(-2)=-4 \pi \\ \quad \Rightarrow \quad y=\pi \cos (2\pi x+4 \pi ).$$