
To find: Identify the polar equation and graph it.

Answer to Problem 58AYU
Solution
The graph of is an equation of Limacon without inner loop.
Given:
It is asked to identify and graph the polar equation .
Explanation of Solution
Check for symmetry test:
Polar axis:
Replace by . The result is
The test satisfied. So the graph is symmetric with respect to the polar axis.
The line
: Replace by . The result is
The test fails, so the graph may or may not symmetric with respect to the line .
The Pole:
Replace by . Then the result is , so . This test fails. Replace by . The result is
This test also fails, so the graph may or may not be symmetric with respect to the pole.
Let’s identify points on the graph by assigning values to the angle and calculating the corresponding values of .
As the polar equation is symmetric about the polar axis, it is enough to find the values from to .
To sketch:
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