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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°.
Related questions
Question
Please graph
![The transcribed mathematical expression from the image is:
\[ y = \frac{1}{2} \sin \left( \frac{1}{3}(\theta - \pi) \right) - 2 \]
This equation appears to be a transformed sine function. Key components to consider for analysis:
1. **Amplitude**: The coefficient \( \frac{1}{2} \) affects the amplitude of the sine wave, reducing it from the standard amplitude of 1 to \( \frac{1}{2} \).
2. **Frequency and Period**: The coefficient \( \frac{1}{3} \) inside the sine function affects the frequency. This changes the period of the sine wave from the standard \( 2\pi \) to \( 6\pi \) since the period is calculated as \( \frac{2\pi}{\frac{1}{3}} \).
3. **Phase Shift**: The term \((\theta - \pi)\) causes a phase shift to the right by \(\pi\) units.
4. **Vertical Shift**: The subtracting 2 at the end of the function shifts the entire graph down by 2 units.
This sine function illustrates various transformations, demonstrating changes in amplitude, period, phase, and vertical position of the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f738a43-0f0f-4966-a050-a7e86ca0ae84%2Fd22e1179-ab87-4ae1-819e-711c02dc6b9f%2Fa0farr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The transcribed mathematical expression from the image is:
\[ y = \frac{1}{2} \sin \left( \frac{1}{3}(\theta - \pi) \right) - 2 \]
This equation appears to be a transformed sine function. Key components to consider for analysis:
1. **Amplitude**: The coefficient \( \frac{1}{2} \) affects the amplitude of the sine wave, reducing it from the standard amplitude of 1 to \( \frac{1}{2} \).
2. **Frequency and Period**: The coefficient \( \frac{1}{3} \) inside the sine function affects the frequency. This changes the period of the sine wave from the standard \( 2\pi \) to \( 6\pi \) since the period is calculated as \( \frac{2\pi}{\frac{1}{3}} \).
3. **Phase Shift**: The term \((\theta - \pi)\) causes a phase shift to the right by \(\pi\) units.
4. **Vertical Shift**: The subtracting 2 at the end of the function shifts the entire graph down by 2 units.
This sine function illustrates various transformations, demonstrating changes in amplitude, period, phase, and vertical position of the graph.
Expert Solution
Step 1
The objective of the question is making the graph of the given function.
Step by step
Solved in 2 steps with 2 images
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