1. **Problem Statement:** Find the period of the sinusoidal function graphed, which oscillates between -5 and 1 on the y-axis and completes one full cycle between consecutive multiples of $\pi$ on the x-axis. 2. **Recall the period formula for cosine functions:** The general form is $f(x) = A \cos(Bx + C) + D$, where the period $T$ is given by: $$T = \frac{2\pi}{|B|}$$ 3. **Analyze the graph:** The function completes one full cycle between consecutive multiples of $\pi$, meaning the period is $\pi$. 4. **Conclusion:** The period of the function is: $$\boxed{\pi}$$ This means the function repeats every $\pi$ units along the x-axis.