Subjects trigonometry

Amplitude Period 562089

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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°.