Subtle symmetry Without using a graphing utility,

Chapter 8, Problem 105AE

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QUESTION:

Without using a graphing utility, determine the symmetries (if any) of the curve \(r = 4-\sin(\theta/2)\).

Questions & Answers

QUESTION:

Without using a graphing utility, determine the symmetries (if any) of the curve \(r = 4-\sin(\theta/2)\).

ANSWER:

Solution 105AE
Step 1:

Symmetry test for polar graphs are:
1. Symmetry about x-axis : If  lies on the graph, the the point also lies on the graph.
2. Symmetry about y-axis : If  lies on the graph, the the point also lies on the graph.
3. Symmetry about origin : If  lies on the graph, the the point also lies on the graph.

Given:

a. Replacing with

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