1. **State the problem:** We are given the graph of the function $y = a \sin(x + b) + c$ for $0 \leq x \leq 360$ degrees. We need to find suitable values for $a$, $b$, and $c$ based on the graph. 2. **Recall the sine function properties:** - The amplitude $a$ is the distance from the midline to the maximum or minimum. - The phase shift $b$ shifts the graph horizontally. - The vertical shift $c$ moves the graph up or down. 3. **Analyze the graph:** - The wave completes one full cycle from $0$ to $360$ degrees, so the period is $360$ degrees. - The maximum value is approximately $4$ and the minimum is approximately $-3$. - The midline is halfway between max and min: $$c = \frac{4 + (-3)}{2} = \frac{1}{2} = 0.5$$ - The amplitude $a$ is half the distance between max and min: $$a = \frac{4 - (-3)}{2} = \frac{7}{2} = 3.5$$ 4. **Determine phase shift $b$:** - The standard sine function $\sin x$ starts at $0$ when $x=0$. - The graph's sine wave starts at the midline going upwards at $x=0$, which matches $\sin x$ with no horizontal shift. - Therefore, $b = 0$. **Final answers:** $$a = 3.5$$ $$b = 0$$ $$c = 0.5$$