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The following graph shows at least one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. y = y 6 5 4 3 2 1 -3 -4 -5 -6 75 2 л 3 л 5 5 4 л 5 бл 7 л | 8 л 9 л 5 5 5 5 2A 5 X

The following graph shows at least one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. y = y 6 5 4 3 2 1 -3 -4 -5 -6 75 2 л 3 л 5 5 4 л 5 бл 7 л | 8 л 9 л 5 5 5 5 2A 5 X

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Trigonometric Functions: Unit Circle Approach
Section6.6: Modeling Harmonic Motion
Problem 44E
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**Trigonometric Functions: Matching the Graph** The following graph shows at least one complete cycle of the graph of an equation containing a trigonometric function. Your task is to find an equation that matches the graph. If you are using a graphing calculator, you can graph your equation to verify its accuracy. ### Graph Description: #### Overview: The graph depicts a red trigonometric curve that resembles a sinusoidal function. The x-axis is labeled with values in terms of \(\pi\), specifically ranging from \( \frac{\pi}{5} \) to \(2\pi\). The y-axis ranges from -6 to 6. #### Key Points: - The graph completes multiple cycles within the interval presented. - Each cycle has a consistent amplitude and wavelength. - The peaks of the graph reach a maximum value of 5. - The troughs of the graph reach a minimum value of -5. - The function crosses the x-axis periodically. #### Axis and Scaling: - **X-Axis**: - The x-axis is labeled in fractional values of \(\pi\). - Specific markers on the x-axis: - \( \frac{\pi}{5} \) - \( \frac{2\pi}{5} \) - \( \frac{3\pi}{5} \) - \( \frac{4\pi}{5} \) - \( \pi \) - \( \frac{6\pi}{5} \) - \( \frac{7\pi}{5} \) - \( \frac{8\pi}{5} \) - \( \frac{9\pi}{5} \) - \( 2\pi \) - **Y-Axis**: - The y-axis ranges from -6 to 6. ### Finding the Equation: Based on the graphical representation, you need to formulate the equation of the trigonometric function that matches this graph. **Equation Format:** \[ y = \] Use your knowledge of trigonometric functions to determine the correct equation. Common trigonometric functions include: - \( \sin(x) \) - \( \cos(x) \) - Variants with different amplitudes, frequencies, and phase shifts. After deriving your equation, verify its accuracy by graphing it on a calculator and using the same parameters to check for a match with the given graph.
Transcribed Image Text:**Trigonometric Functions: Matching the Graph** The following graph shows at least one complete cycle of the graph of an equation containing a trigonometric function. Your task is to find an equation that matches the graph. If you are using a graphing calculator, you can graph your equation to verify its accuracy. ### Graph Description: #### Overview: The graph depicts a red trigonometric curve that resembles a sinusoidal function. The x-axis is labeled with values in terms of \(\pi\), specifically ranging from \( \frac{\pi}{5} \) to \(2\pi\). The y-axis ranges from -6 to 6. #### Key Points: - The graph completes multiple cycles within the interval presented. - Each cycle has a consistent amplitude and wavelength. - The peaks of the graph reach a maximum value of 5. - The troughs of the graph reach a minimum value of -5. - The function crosses the x-axis periodically. #### Axis and Scaling: - **X-Axis**: - The x-axis is labeled in fractional values of \(\pi\). - Specific markers on the x-axis: - \( \frac{\pi}{5} \) - \( \frac{2\pi}{5} \) - \( \frac{3\pi}{5} \) - \( \frac{4\pi}{5} \) - \( \pi \) - \( \frac{6\pi}{5} \) - \( \frac{7\pi}{5} \) - \( \frac{8\pi}{5} \) - \( \frac{9\pi}{5} \) - \( 2\pi \) - **Y-Axis**: - The y-axis ranges from -6 to 6. ### Finding the Equation: Based on the graphical representation, you need to formulate the equation of the trigonometric function that matches this graph. **Equation Format:** \[ y = \] Use your knowledge of trigonometric functions to determine the correct equation. Common trigonometric functions include: - \( \sin(x) \) - \( \cos(x) \) - Variants with different amplitudes, frequencies, and phase shifts. After deriving your equation, verify its accuracy by graphing it on a calculator and using the same parameters to check for a match with the given graph.
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