1. The problem asks to find an expression for $f(x)$ in the form $f(x) = a \cdot \sin(x - b)$ where $a$ is the amplitude and $b \in \mathbb{Z}$. 2. From the graph description, the amplitude $a$ is the maximum absolute value of $f(x)$, which is 4. 3. The period of the sine function is $360^\circ$, and the graph repeats every $360^\circ$. 4. To find the phase shift $b$, observe where the sine wave crosses zero going upwards. The sine function $\sin(x)$ crosses zero at $x=0$, but here it crosses zero at $x=180^\circ$, so the phase shift is $b=180$. 5. Therefore, the sine form is: $$f(x) = 4 \cdot \sin(x - 180)$$ 6. Next, find an expression for $f(x)$ in the form $f(x) = a \cdot \cos(x - b)$ where $a,b \in \mathbb{Z}$. 7. The amplitude $a$ remains 4. 8. The cosine function $\cos(x)$ has its maximum at $x=0$. From the graph, the maximum occurs at $x=270^\circ$, so the phase shift $b=270$. 9. Therefore, the cosine form is: $$f(x) = 4 \cdot \cos(x - 270)$$