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9. y= sin (r - (z+ 10. y = sin 4 11. y = cos (x – 4. (z + 12. y = coS 13. y = 1+ sin x 14. y = -1+ sin a 15. y = 1+ cos z 16. y = -1+ cos x

9. y= sin (r - (z+ 10. y = sin 4 11. y = cos (x – 4. (z + 12. y = coS 13. y = 1+ sin x 14. y = -1+ sin a 15. y = 1+ cos z 16. y = -1+ cos x

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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Match each function with its graph ( only part 10,12, 14)
This image presents a collection of nine different graphs labeled from A to I, depicting various trigonometric functions, likely sinusoidal in nature. Each graph features an x and y axis with specific markings related to the function's period and amplitude. ### Graph Details: - **Graph A**: - The graph shows a sinusoidal curve with its key points marked on the x-axis at \( \frac{\pi}{4} \) intervals, extending from 0 to \( \frac{7\pi}{4} \). - The y-axis spans from -1 to 1, indicating amplitude. - **Graph B**: - This graph has critical points marked from \( \frac{\pi}{2} \) to \( 2\pi \). - The amplitude varies from -1 to 1. - **Graph C**: - The x-axis is labeled from 0 to \( 2\pi \) with key sinusoidal turning points. - Y-values range from -2 to 1, suggesting a different scaling in amplitude compared to the others. - **Graph D**: - Displays a classic wave with the period marked from 0 to \( \frac{9\pi}{4} \). - The amplitude range is from -1 to 1. - **Graph E**: - Illustrated with points starting from 0 and extending to \( 2\pi \). - It has a y-range from -2 to 1, indicating its amplitude diversifies from typical sine or cosine graphs. - **Graph F**: - This harmonic function stretches from 0 to \( 2\pi \) on the x-axis. - The amplitude ranges from 0 to 2 on the y-axis, suggesting a positive vertical shift. - **Graph G**: - The function has intervals marked from \(-\frac{\pi}{4}\) through to \(\frac{7\pi}{4}\). - The y-axis ranges from -1 to 1. - **Graph H**: - Key intervals on the x-axis are marked starting from 0 extending to \( \frac{9\pi}{4} \). - The range for y-values is from -1 to 1. - **Graph I**: - The x-axis runs from 0 to \( 2\pi \). - An amplitude from -1 to
Transcribed Image Text:This image presents a collection of nine different graphs labeled from A to I, depicting various trigonometric functions, likely sinusoidal in nature. Each graph features an x and y axis with specific markings related to the function's period and amplitude. ### Graph Details: - **Graph A**: - The graph shows a sinusoidal curve with its key points marked on the x-axis at \( \frac{\pi}{4} \) intervals, extending from 0 to \( \frac{7\pi}{4} \). - The y-axis spans from -1 to 1, indicating amplitude. - **Graph B**: - This graph has critical points marked from \( \frac{\pi}{2} \) to \( 2\pi \). - The amplitude varies from -1 to 1. - **Graph C**: - The x-axis is labeled from 0 to \( 2\pi \) with key sinusoidal turning points. - Y-values range from -2 to 1, suggesting a different scaling in amplitude compared to the others. - **Graph D**: - Displays a classic wave with the period marked from 0 to \( \frac{9\pi}{4} \). - The amplitude range is from -1 to 1. - **Graph E**: - Illustrated with points starting from 0 and extending to \( 2\pi \). - It has a y-range from -2 to 1, indicating its amplitude diversifies from typical sine or cosine graphs. - **Graph F**: - This harmonic function stretches from 0 to \( 2\pi \) on the x-axis. - The amplitude ranges from 0 to 2 on the y-axis, suggesting a positive vertical shift. - **Graph G**: - The function has intervals marked from \(-\frac{\pi}{4}\) through to \(\frac{7\pi}{4}\). - The y-axis ranges from -1 to 1. - **Graph H**: - Key intervals on the x-axis are marked starting from 0 extending to \( \frac{9\pi}{4} \). - The range for y-values is from -1 to 1. - **Graph I**: - The x-axis runs from 0 to \( 2\pi \). - An amplitude from -1 to
In this educational content, we explore various transformations of the sine and cosine functions. Each function is presented with its respective mathematical form. 1. **\( y = \sin \left( x - \frac{\pi}{4} \right) \)** - This function represents a sine wave shifted to the right by \(\frac{\pi}{4}\). 2. **\( y = \sin \left( x + \frac{\pi}{4} \right) \)** - This function represents a sine wave shifted to the left by \(\frac{\pi}{4}\). 3. **\( y = \cos \left( x - \frac{\pi}{4} \right) \)** - This function represents a cosine wave shifted to the right by \(\frac{\pi}{4}\). 4. **\( y = \cos \left( x + \frac{\pi}{4} \right) \)** - This function represents a cosine wave shifted to the left by \(\frac{\pi}{4}\). 5. **\( y = 1 + \sin x \)** - This function is a vertical translation of the sine wave, moved up by 1 unit. 6. **\( y = -1 + \sin x \)** - This function is a vertical translation of the sine wave, moved down by 1 unit. 7. **\( y = 1 + \cos x \)** - This function is a vertical translation of the cosine wave, moved up by 1 unit. 8. **\( y = -1 + \cos x \)** - This function is a vertical translation of the cosine wave, moved down by 1 unit. These transformations illustrate how shifting and translation affect the properties of sine and cosine functions in trigonometry, aiding in analysis and application in various mathematical contexts.
Transcribed Image Text:In this educational content, we explore various transformations of the sine and cosine functions. Each function is presented with its respective mathematical form. 1. **\( y = \sin \left( x - \frac{\pi}{4} \right) \)** - This function represents a sine wave shifted to the right by \(\frac{\pi}{4}\). 2. **\( y = \sin \left( x + \frac{\pi}{4} \right) \)** - This function represents a sine wave shifted to the left by \(\frac{\pi}{4}\). 3. **\( y = \cos \left( x - \frac{\pi}{4} \right) \)** - This function represents a cosine wave shifted to the right by \(\frac{\pi}{4}\). 4. **\( y = \cos \left( x + \frac{\pi}{4} \right) \)** - This function represents a cosine wave shifted to the left by \(\frac{\pi}{4}\). 5. **\( y = 1 + \sin x \)** - This function is a vertical translation of the sine wave, moved up by 1 unit. 6. **\( y = -1 + \sin x \)** - This function is a vertical translation of the sine wave, moved down by 1 unit. 7. **\( y = 1 + \cos x \)** - This function is a vertical translation of the cosine wave, moved up by 1 unit. 8. **\( y = -1 + \cos x \)** - This function is a vertical translation of the cosine wave, moved down by 1 unit. These transformations illustrate how shifting and translation affect the properties of sine and cosine functions in trigonometry, aiding in analysis and application in various mathematical contexts.
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Matching the graph of functions given by questions 10, 12 and 14

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