To find: Identify the polar equation and graph it.
Answer to Problem 56AYU
Solution
The graph of is an equation of Spiral.
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 fails, so the graph may or may not 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.
Furthermore, there is no number for which , so the graph does not pass through the pole. Observe that is positive for all , increases as increases, as .
Let’s find the values from to to get single line spiral.
To sketch:
.
Chapter 9 Solutions
Precalculus
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