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6. Which of the following graphs shows the relationship between the frequency, B, and the period, P, of a sinusoidal graph? Experiment on your calculator. Graph the expression P= В (1) (3) (4) В

6. Which of the following graphs shows the relationship between the frequency, B, and the period, P, of a sinusoidal graph? Experiment on your calculator. Graph the expression P= В (1) (3) (4) В

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Understanding the Relationship Between Frequency and Period of a Sinusoidal Graph --- **Question 6**: Which of the following graphs shows the relationship between the frequency, \( B \), and the period, \( P \), of a sinusoidal graph? Experiment on your calculator. Graph the expression \( P = \frac{2\pi}{B} \). **Graphs to Consider**: 1. **Graph (1)**: This graph shows a curve starting at the highest point on the \( P \) (y) axis and asymptotically approaching the \( B \) (x) axis, resembling the first quadrant of a circle. 2. **Graph (2)**: This shows an upward-curving graph starting low on both axes and extending towards the higher values of \( P \) and \( B \). 3. **Graph (3)**: This shows a hyperbolic graph decreasing from a high value on the \( P \) axis and asymptotically approaching the \( B \) axis. 4. **Graph (4)**: Depicts a linear graph with a negative slope, starting high on the \( P \) axis and descending towards the \( B \) axis. ### Detailed Explanation The problem requires identifying the correct graph of the expression \( P = \frac{2\pi}{B} \). This represents the inverse relationship between period \( P \) and frequency \( B \) for sinusoidal functions. - **Expression Analysis**: - The period \( P \) is inversely proportional to the frequency \( B \). As \( B \) increases, \( P \) decreases. - The formula \( P = \frac{2\pi}{B} \) illustrates a hyperbolic graph. **Correct Graph**: - **Graph (3)** accurately demonstrates this inverse relationship. As \( B \) on the x-axis increases, \( P \) on the y-axis decreases hyperbolically, which aligns with the equation \( P = \frac{2\pi}{B} \). #### Key Characteristics of the Correct Graph (Graph 3): - Starts at a high value on the \( P \) axis. - Decreases towards zero as values on the \( B \) axis increase.
Transcribed Image Text:### Understanding the Relationship Between Frequency and Period of a Sinusoidal Graph --- **Question 6**: Which of the following graphs shows the relationship between the frequency, \( B \), and the period, \( P \), of a sinusoidal graph? Experiment on your calculator. Graph the expression \( P = \frac{2\pi}{B} \). **Graphs to Consider**: 1. **Graph (1)**: This graph shows a curve starting at the highest point on the \( P \) (y) axis and asymptotically approaching the \( B \) (x) axis, resembling the first quadrant of a circle. 2. **Graph (2)**: This shows an upward-curving graph starting low on both axes and extending towards the higher values of \( P \) and \( B \). 3. **Graph (3)**: This shows a hyperbolic graph decreasing from a high value on the \( P \) axis and asymptotically approaching the \( B \) axis. 4. **Graph (4)**: Depicts a linear graph with a negative slope, starting high on the \( P \) axis and descending towards the \( B \) axis. ### Detailed Explanation The problem requires identifying the correct graph of the expression \( P = \frac{2\pi}{B} \). This represents the inverse relationship between period \( P \) and frequency \( B \) for sinusoidal functions. - **Expression Analysis**: - The period \( P \) is inversely proportional to the frequency \( B \). As \( B \) increases, \( P \) decreases. - The formula \( P = \frac{2\pi}{B} \) illustrates a hyperbolic graph. **Correct Graph**: - **Graph (3)** accurately demonstrates this inverse relationship. As \( B \) on the x-axis increases, \( P \) on the y-axis decreases hyperbolically, which aligns with the equation \( P = \frac{2\pi}{B} \). #### Key Characteristics of the Correct Graph (Graph 3): - Starts at a high value on the \( P \) axis. - Decreases towards zero as values on the \( B \) axis increase.
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