Determine the amplitude of the following graph. 4 3 2 सोजयेषीन 1 47 3 -27 27 3 3 6. -1 3 6. -2 -3 -4 -5

Trigonometry (MindTap Course List)
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Author:Ron Larson
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Chapter1: Trigonometry
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Problem 20T: A ball on a spring starts at its lowest point of 6 inches below equilibrium, bounces to its maximum...
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**Determine the amplitude of the following graph.**

This image presents a graph of a periodic function. The horizontal axis (x-axis) is marked with values representing multiples of π, ranging from \(- \frac{4π}{3}\) to \(\frac{4π}{3}\). The vertical axis (y-axis) is labeled from -5 to 5. 

The function plotted on the graph oscillates above and below the x-axis, indicating the characteristic pattern of a trigonometric function like sine or cosine.

### Detailed Analysis:
1. **X-Axis Units:**
   - The x-axis includes specific points marked as \(- \frac{4π}{3}\), \(- π\), \(- \frac{π}{2} \),  0, \( \frac{π}{2} \), \( π \), \(\frac{3π}{2}\), \(2π\).
  
2. **Y-Axis Units:**
   - The y-axis ranges from -5 to 5 in increments of 1.

3. **Wave Characteristics:**
   - The peaks and valleys of the wave are key to determining the amplitude.
   - The highest points (peaks) of the wave reach a value of 1 on the y-axis.
   - The lowest points (valleys) of the wave dip down to -1 on the y-axis.

### Amplitude Calculation:
The amplitude of a wave is the distance from the center line (equilibrium position) to a peak or a valley. In this graph:

- The center line is at y = 0.
- The peak is at y = 1.
- The valley is at y = -1.

Hence, the amplitude (A) is:

\[ A = \text{Peak} - \text{Center Line} = 1 - 0 = 1 \]

\[ A = \text{Valley} - \text{Center Line} = -1 - 0 = 1 \]

Therefore, the amplitude of the given graph is 1.
Transcribed Image Text:**Determine the amplitude of the following graph.** This image presents a graph of a periodic function. The horizontal axis (x-axis) is marked with values representing multiples of π, ranging from \(- \frac{4π}{3}\) to \(\frac{4π}{3}\). The vertical axis (y-axis) is labeled from -5 to 5. The function plotted on the graph oscillates above and below the x-axis, indicating the characteristic pattern of a trigonometric function like sine or cosine. ### Detailed Analysis: 1. **X-Axis Units:** - The x-axis includes specific points marked as \(- \frac{4π}{3}\), \(- π\), \(- \frac{π}{2} \), 0, \( \frac{π}{2} \), \( π \), \(\frac{3π}{2}\), \(2π\). 2. **Y-Axis Units:** - The y-axis ranges from -5 to 5 in increments of 1. 3. **Wave Characteristics:** - The peaks and valleys of the wave are key to determining the amplitude. - The highest points (peaks) of the wave reach a value of 1 on the y-axis. - The lowest points (valleys) of the wave dip down to -1 on the y-axis. ### Amplitude Calculation: The amplitude of a wave is the distance from the center line (equilibrium position) to a peak or a valley. In this graph: - The center line is at y = 0. - The peak is at y = 1. - The valley is at y = -1. Hence, the amplitude (A) is: \[ A = \text{Peak} - \text{Center Line} = 1 - 0 = 1 \] \[ A = \text{Valley} - \text{Center Line} = -1 - 0 = 1 \] Therefore, the amplitude of the given graph is 1.
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