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the following equations represents the graph shown?

the following equations represents the graph shown?

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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### Graph Analysis and Equation Identification **Question:** Which of the following equations represents the graph shown? **Graph Description:** The graph displayed features a sinusoidal wave (sine or cosine wave) starting from the point (0,3), peaking at (π/2, 5), reaching a low point at (3π/2, 1), and then peaking again. The wave continues to oscillate in this manner. **Equations to Choose From:** 1. \( y = -2 \sin \left( x - \frac{\pi}{6} \right) + 3 \) 2. \( y = -2 \cos \left( x - \frac{\pi}{6} \right) + 3 \) 3. \( y = 2 \sin \left( x + \frac{\pi}{6} \right) + 3 \) 4. \( y = 2 \cos \left( x + \frac{\pi}{6} \right) + 3 \) 5. \( y = 2 \cos \left( x - \frac{\pi}{6} \right) + 3 \) **Explanation:** - The graph has a vertical shift of +3, as the midline of the wave is at y = 3. - The amplitude of the wave is 2, showing the height of the wave from the midline to the peak or to the trough. - The graph appears to be a cosine wave since it starts at a maximum point. - There is a horizontal shift in the graph. **Conclusion:** - The correct equation that matches the graph is \( y = 2 \cos \left( x - \frac{\pi}{6} \right) + 3 \). **Navigation:** This is part of an online test or quiz interface, with navigation buttons allowing users to go to the previous page (arrow pointing left) or proceed to the next page (Next >). There is a horizontal navigation bar at the bottom indicating page numbers, and the current page is 13 out of 16 pages.
Transcribed Image Text:### Graph Analysis and Equation Identification **Question:** Which of the following equations represents the graph shown? **Graph Description:** The graph displayed features a sinusoidal wave (sine or cosine wave) starting from the point (0,3), peaking at (π/2, 5), reaching a low point at (3π/2, 1), and then peaking again. The wave continues to oscillate in this manner. **Equations to Choose From:** 1. \( y = -2 \sin \left( x - \frac{\pi}{6} \right) + 3 \) 2. \( y = -2 \cos \left( x - \frac{\pi}{6} \right) + 3 \) 3. \( y = 2 \sin \left( x + \frac{\pi}{6} \right) + 3 \) 4. \( y = 2 \cos \left( x + \frac{\pi}{6} \right) + 3 \) 5. \( y = 2 \cos \left( x - \frac{\pi}{6} \right) + 3 \) **Explanation:** - The graph has a vertical shift of +3, as the midline of the wave is at y = 3. - The amplitude of the wave is 2, showing the height of the wave from the midline to the peak or to the trough. - The graph appears to be a cosine wave since it starts at a maximum point. - There is a horizontal shift in the graph. **Conclusion:** - The correct equation that matches the graph is \( y = 2 \cos \left( x - \frac{\pi}{6} \right) + 3 \). **Navigation:** This is part of an online test or quiz interface, with navigation buttons allowing users to go to the previous page (arrow pointing left) or proceed to the next page (Next >). There is a horizontal navigation bar at the bottom indicating page numbers, and the current page is 13 out of 16 pages.
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