Explanation Check for symmetry test: Polar axis: Replace θ by − θ . The result is r = 1 − 3 cos ( − θ ) = 1 − 3 cos θ The test satisfied. So the graph is symmetric with respect to the polar axis. The line θ = π 2 : Replace θ by π − θ . The result is r = 1 − 3 cos ( π − θ ) = 1 − 3 ( cos π cos θ + sin π sin θ ) = 1 − 3 ( ( − 1 ) cos θ + ( 0 ) sin θ ) = 1 + 3 cos θ The test fails, so the graph may or may not symmetric with respect to the line θ = π 2 . The Pole: Replace r by − r . Then the result is − r = 1 − 3 cos θ , so r = − 1 + 3 cos θ . This test fails. Replace θ by θ + π . The result is r = 1 − 3 cos ( θ + π ) = 1 − 3 ( cos π cos θ − sin π sin θ ) = 1 − 3 ( − 1 ) cos θ = 1 + 3 cos θ . 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 θ and calculating the corresponding values of r . As the polar equation is symmetric about the polar axis, it is enough to find the values from 0 to π ...

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Author: Michael Sullivan

Publisher: PEARSON

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Chapter 9.2, Problem 61AYU

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Chapter 9.2, Problem 60AYU

Chapter 9.2, Problem 62AYU

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Identify the polar equation r = 1 − 3 cos θ and graph it.

Solution Summary: The author explains how the graph of r = 1 3 cos is symmetric with respect to the polar axis.

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To find: Identify the polar equation $r = 1 - 3 cos θ$ and graph it.

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Chapter 9 Solutions

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Identify the polar equation r = 1 − 3 cos θ and graph it.

Solution Summary: The author explains how the graph of r = 1 3 cos is symmetric with respect to the polar axis.

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To find: Identify the polar equation r = 1 − 3 cos θ and graph it.

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Chapter 9 Solutions

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To find: Identify the polar equation $r = 1 - 3 cos θ$ and graph it.