QQuestionMathematics
QuestionMathematics
# Question 3 of 10
## 2 Points
Which features are present in this polar graph?
$\square$ A. Symmetry about the pole $(0,0)$
$\square$ B. No symmetry
$\square$ C. Symmetry about the polar axis $\theta= 0$
$\square$ D. Symmetry about the line $\theta=\frac{\pi}{2}$
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Answer
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Step 1:I'll solve this step by step, analyzing the polar graph's symmetry carefully.
Step 2:: Understand Symmetry in Polar Graphs
- Symmetry about the line $$\theta = \frac{\pi}{2}
In polar coordinates, symmetry can occur in several ways: - Symmetry about the pole (0,0)
Step 3:: Visual Inspection of the Graph
- About line $$\theta = \frac{\pi}{2}$$:
Looking at the graph, I'll check each potential symmetry type: - About the pole (0,0): If the graph looks the same when rotated 180°, this symmetry exists. If the graph looks the same when reflected across the horizontal axis. If the graph looks the same when reflected across the vertical axis.
Step 4:: Detailed Analysis
Carefully examining the graph, I observe: - The graph appears identical when rotated 180° around the pole - This indicates symmetry about the pole (0,0)
Step 5:: Eliminate Other Options
- This rules out symmetry about the polar axis or $$\theta = \frac{\pi}{2}
- The graph does NOT look the same when reflected across horizontal or vertical axes
Final Answer
Symmetry about the pole (0,0)
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