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,...
Related questions
Question
11
![**Graph Two Periods of the Given Cosecant Function**
**Function:**
\[ y = \frac{1}{2} \csc\left(\frac{x}{2}\right) \]
**Task:**
Choose the correct graph below.
**Graph Options:**
- **Option A:**
- The graph shows a series of upward and downward curves traditionally associated with the cosecant function, extending vertically beyond the graph grid.
- The curves appear to be evenly spaced, with two full cycles visible.
- X-axis labeled with marks at intervals.
- Y-axis extends from -5 to 5.
- **Option B:**
- Similar pattern as Option A, but placement of curves may differ, indicating potential shifts in interval or phase.
- Features two full cycles of the cosecant function.
- X and Y axes are labeled similarly, extending over the same range.
- **Option C:**
- Exhibits similar vertical wave patterns of the cosecant function.
- The graph reflects shifts or alterations in direction, evident in the position of poles and maximum amplitude.
- Maintains consistent axis scales as the other options.
**Instructions:**
Evaluate the graphs based on your understanding of the cosecant function and select the correct graph that represents the function for two periods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c90df0f-14a9-4ebc-bcd9-ac76e31a33b9%2Fc618058d-9e73-45f2-a0d4-f8725c5cf343%2Fqnldk3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph Two Periods of the Given Cosecant Function**
**Function:**
\[ y = \frac{1}{2} \csc\left(\frac{x}{2}\right) \]
**Task:**
Choose the correct graph below.
**Graph Options:**
- **Option A:**
- The graph shows a series of upward and downward curves traditionally associated with the cosecant function, extending vertically beyond the graph grid.
- The curves appear to be evenly spaced, with two full cycles visible.
- X-axis labeled with marks at intervals.
- Y-axis extends from -5 to 5.
- **Option B:**
- Similar pattern as Option A, but placement of curves may differ, indicating potential shifts in interval or phase.
- Features two full cycles of the cosecant function.
- X and Y axes are labeled similarly, extending over the same range.
- **Option C:**
- Exhibits similar vertical wave patterns of the cosecant function.
- The graph reflects shifts or alterations in direction, evident in the position of poles and maximum amplitude.
- Maintains consistent axis scales as the other options.
**Instructions:**
Evaluate the graphs based on your understanding of the cosecant function and select the correct graph that represents the function for two periods.
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