For the second picture, evaluate g(6). Graph g(x) on the interval [0, 42].
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
For the second picture, evaluate g(6). Graph g(x) on the interval [0, 42].
![**Educational Task Instructions**
**Enter the exact answer**.
\( g(6) = \) [Number Input Field]
---
**Question c**: What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond?
The minimum distance between the comet and Earth is [Number Input Field] km which is the [Drop-down List] constant. It occurs at [Number Input Field] days.
---
**Question d**: Find and discuss the meaning of any vertical asymptotes on the interval \([0, 42]\).
The field below accepts a list of numbers or formulas separated by semicolons (e.g. \( 2; 4; 6 \) or \( x + 1; x - 1 \)). The order of the list does not matter.
\( x = \) [Input Field with Calculator]
At the vertical asymptotes the comet is [Drop-down List].
---
**Note**: Each field and list is an interactive input where students need to enter or select the appropriate answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54422bad-1dbc-44f7-b929-730cc42f6e53%2Fe2574aa2-74f5-4dda-ae81-75f8502511ab%2Fiedxom_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Task Instructions**
**Enter the exact answer**.
\( g(6) = \) [Number Input Field]
---
**Question c**: What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond?
The minimum distance between the comet and Earth is [Number Input Field] km which is the [Drop-down List] constant. It occurs at [Number Input Field] days.
---
**Question d**: Find and discuss the meaning of any vertical asymptotes on the interval \([0, 42]\).
The field below accepts a list of numbers or formulas separated by semicolons (e.g. \( 2; 4; 6 \) or \( x + 1; x - 1 \)). The order of the list does not matter.
\( x = \) [Input Field with Calculator]
At the vertical asymptotes the comet is [Drop-down List].
---
**Note**: Each field and list is an interactive input where students need to enter or select the appropriate answer.
![### Distance of a Comet from Earth Over Time
A laser rangefinder is locked on a comet approaching Earth. The distance \( g(x) \), in kilometers, of the comet after \( x \) days, for \( x \) in the interval \( 0 \) to \( 36 \) days, is given by the function:
\[ g(x) = 350{,}000 \csc\left(\frac{\pi}{36} x \right) \]
#### Task:
**a. Select the graph of \( g(x) \) on the interval \([0, 42]\).**
#### Description of Graphs:
**Graph 1:**
- The graph shows the function \( g(x) \) plotted over the interval \([0, 42]\).
- The y-axis ranges from \( -1 \times 10^7 \) to \( 1 \times 10^7 \).
- The x-axis ranges from 0 to 42.
- There is a significant near-vertical asymptote at \( x = 36 \) due to the nature of the cosecant function.
- The graph appears to tend towards infinity and negative infinity near \( x = 36 \), indicating points of discontinuity or undefined values. The function values rapidly change near this point.
- The function continuously fluctuates, indicating the periodic nature of the cosecant function.
**Graph 2:**
- This graph also shows the function \( g(x) \) plotted over the interval \([0, 42]\).
- The y-axis ranges from \( -1 \times 10^7 \) to \( 1 \times 10^7 \).
- The x-axis also ranges from 0 to 42.
- There is a near-vertical asymptote at \( x = 36 \), showcasing large positive and negative values near this point, similar to Graph 1.
- The fluctuation in function values is apparent, displaying the periodicity as well.
### Selecting the Correct Graph:
Analyzing both graphs, the key differences and behaviors of the function \( g(x) \) near the interval boundaries and points where the cosecant function is undefined should be considered carefully.
Users are encouraged to select the graph that accurately depicts these characteristics in the context given.
#### Additional Notes:
- The csc function, being the reciprocal of the sine function, will approach positive or negative infinity wherever the sine](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54422bad-1dbc-44f7-b929-730cc42f6e53%2Fe2574aa2-74f5-4dda-ae81-75f8502511ab%2Flz2hnom_processed.png&w=3840&q=75)
Transcribed Image Text:### Distance of a Comet from Earth Over Time
A laser rangefinder is locked on a comet approaching Earth. The distance \( g(x) \), in kilometers, of the comet after \( x \) days, for \( x \) in the interval \( 0 \) to \( 36 \) days, is given by the function:
\[ g(x) = 350{,}000 \csc\left(\frac{\pi}{36} x \right) \]
#### Task:
**a. Select the graph of \( g(x) \) on the interval \([0, 42]\).**
#### Description of Graphs:
**Graph 1:**
- The graph shows the function \( g(x) \) plotted over the interval \([0, 42]\).
- The y-axis ranges from \( -1 \times 10^7 \) to \( 1 \times 10^7 \).
- The x-axis ranges from 0 to 42.
- There is a significant near-vertical asymptote at \( x = 36 \) due to the nature of the cosecant function.
- The graph appears to tend towards infinity and negative infinity near \( x = 36 \), indicating points of discontinuity or undefined values. The function values rapidly change near this point.
- The function continuously fluctuates, indicating the periodic nature of the cosecant function.
**Graph 2:**
- This graph also shows the function \( g(x) \) plotted over the interval \([0, 42]\).
- The y-axis ranges from \( -1 \times 10^7 \) to \( 1 \times 10^7 \).
- The x-axis also ranges from 0 to 42.
- There is a near-vertical asymptote at \( x = 36 \), showcasing large positive and negative values near this point, similar to Graph 1.
- The fluctuation in function values is apparent, displaying the periodicity as well.
### Selecting the Correct Graph:
Analyzing both graphs, the key differences and behaviors of the function \( g(x) \) near the interval boundaries and points where the cosecant function is undefined should be considered carefully.
Users are encouraged to select the graph that accurately depicts these characteristics in the context given.
#### Additional Notes:
- The csc function, being the reciprocal of the sine function, will approach positive or negative infinity wherever the sine
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