Question

question 10, 6.4.19
part 1 of 4
hw score: 48.44%, 7.75
of 16 points
points: 0 of 1
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test for symmetry and then graph the polar equation.
r = 1 - cosθ
a. is the graph of the polar equation symmetric with respect to the polar axis?
a. the polar equation failed the test for symmetry which means that the graph is not
symmetric with respect to the polar axis.
b. yes.
c. the polar equation failed the test for symmetry which means that the graph may or may
not be symmetric with respect to the polar axis.

Explanation:

Step1: Test symmetry about polar axis

Replace \(\theta\) with \(-\theta\) in \(r = 1-\cos\theta\).
Since \(\cos(-\theta)=\cos\theta\), we get \(r = 1-\cos(-\theta)=1 - \cos\theta\).
The equation remains the same.

Answer:

B. Yes.