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A polar graph of is given over the stated interval. Sketch the graph of
Text solutionVerified
Key Concepts: Polar Coordinates, Graphing Polar Functions
Explanation:
To sketch the graph of a polar function with respect to a given angle, we replace all instances of θ with (θ ± kπ/2), where k is an odd integer for (a), (b) and (c) and even integer for (d).
Step by Step Solution:
Step 1. Plot the graph of r=f(θ) for the given interval
Step 2. {'option_a': 'Plot the graph of r=f(-θ) for the given interval by replacing θ with -θ and use odd symmetry by drawing the mirror image representation of f(θ) about the vertical axis.', 'option_b': 'Plot the graph of r=f(θ-π/2) for the given interval by replacing θ with (θ - π/2) and use the fact that this transformation corresponds to a clockwise rotation of π/2 about the origin.', 'option_c': 'Plot the graph of r=f(θ + π/2) for the given interval by replacing θ with (θ + π/2) and use the fact that this transformation corresponds to a counterclockwise rotation of π/2 about the origin.', 'option_d': 'Plot the graph of r=-f(θ) for the given interval by multiplying the output of f(θ) by -1 before graphing and notice that this transformation corresponds to a reflection about the origin.'}
Step 3. Label the graphs appropriately and indicate any key features such as symmetry, intercepts, or asymptotes.
Step 4. Final Answer: The sketch of graphs in (a), (b), (c) and (d) are as per the individual transformations.
Final Answer:
The sketch of graphs in (a), (b), (c) and (d) are as per the individual transformations.
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Question Text | A polar graph of is given over the stated interval. Sketch the graph of |
Topic | All topics |
Subject | Chemistry |
Class | Class 12 |
Answer Type | Text solution:1 |