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1 4 6. 7 Write the equation of a sine or cosine function to describe the graph. 5- 4. 2- 00

1 4 6. 7 Write the equation of a sine or cosine function to describe the graph. 5- 4. 2- 00

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 14E
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**Write the equation of a sine or cosine function to describe the graph.** The image shows a trigonometric graph that resembles the sine or cosine function. The graph appears to oscillate between -3 and 3 on the y-axis. **Graph Description:** - **Amplitude**: The maximum height from the centerline (y = 0) to the peak is 3, which indicates an amplitude of 3. - **Period**: The graph completes one full cycle from negative to positive and back over a horizontal distance of 4 units. This suggests the period is 4. - **Vertical Shift**: The graph is centered on the y-axis, implying no vertical shift. - **Horizontal Shift**: The peak at x = 0 suggests it may be a sine function with no horizontal shift or a cosine function shifted to the left by 1 unit. These characteristics can be used to form either a sine or cosine function equation: - **Sine Function**: \( y = 3 \sin\left(\frac{\pi}{2} x\right) \) - **Cosine Function**: \( y = 3 \cos\left(\frac{\pi}{2} (x + 1)\right) \) Both forms describe the same graph.
Transcribed Image Text:**Write the equation of a sine or cosine function to describe the graph.** The image shows a trigonometric graph that resembles the sine or cosine function. The graph appears to oscillate between -3 and 3 on the y-axis. **Graph Description:** - **Amplitude**: The maximum height from the centerline (y = 0) to the peak is 3, which indicates an amplitude of 3. - **Period**: The graph completes one full cycle from negative to positive and back over a horizontal distance of 4 units. This suggests the period is 4. - **Vertical Shift**: The graph is centered on the y-axis, implying no vertical shift. - **Horizontal Shift**: The peak at x = 0 suggests it may be a sine function with no horizontal shift or a cosine function shifted to the left by 1 unit. These characteristics can be used to form either a sine or cosine function equation: - **Sine Function**: \( y = 3 \sin\left(\frac{\pi}{2} x\right) \) - **Cosine Function**: \( y = 3 \cos\left(\frac{\pi}{2} (x + 1)\right) \) Both forms describe the same graph.
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