Question: What is the correct amplitude and period in the following graph:
Amplitude: 2; period: 120°
Amplitude: 2; period: 60°
Amplitude: 8; period: 60°
Amplitude: 4; period: 120°
Graph shape and math: a sinusoidal wave centered at y = -1 with maximum near y = 1 and minimum near y = -3, so amplitude is 2; consecutive peaks occur about 120° apart, so period is 120°.
1. **State the problem:** Determine the amplitude and period of the sinusoidal wave described.
2. **Recall the definitions:**
- Amplitude is the distance from the midline (center) to a peak or trough.
- Period is the horizontal length of one complete cycle of the wave.
3. **Analyze the given data:**
- The wave is centered at $y = -1$.
- Maximum value is near $y = 1$.
- Minimum value is near $y = -3$.
4. **Calculate amplitude:**
$$\text{Amplitude} = \text{max} - \text{center} = 1 - (-1) = 2$$
5. **Calculate period:**
- Consecutive peaks occur about $120^\circ$ apart.
- Therefore, $$\text{Period} = 120^\circ$$
6. **Conclusion:**
- Amplitude is $2$.
- Period is $120^\circ$.
Hence, the correct choice is: Amplitude: 2; period: 120°.