1. The problem asks for the period of the function $y = 2 \cos\left(\frac{x}{3}\right) - 1$. 2. Recall the general form of a cosine function: $y = A \cos(Bx - C) + D$. 3. The period of a cosine function is given by the formula: $$\text{Period} = \frac{360^\circ}{|B|}$$ 4. In our function, the argument of cosine is $\frac{x}{3}$, which can be rewritten as $\left(\frac{1}{3}\right)x$. So, $B = \frac{1}{3}$. 5. Substitute $B = \frac{1}{3}$ into the period formula: $$\text{Period} = \frac{360^\circ}{\left|\frac{1}{3}\right|} = 360^\circ \times 3 = 1080^\circ$$ 6. Therefore, the period of $y = 2 \cos\left(\frac{x}{3}\right) - 1$ is $1080^\circ$. Final answer: The period is $1080^\circ$.