Explanation Check for symmetry test: Polar axis: Replace θ by − θ . The result is r = 3 ( − θ ) = 3 − θ . The test fails, so the graph may or may not symmetric with respect to the polar axis. The line θ = π 2 : Replace θ by π − θ . The result is r = 3 π − θ = 3 π .3 − θ = 3 π 3 θ = 31.54 3 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 = 3 θ , so r = − 3 θ , This test fails. Replace θ by θ + π . The result is r = 3 θ + π = 3 θ .3 π = 31.54.3 θ . This test also fails, so the graph may or may not be symmetric with respect to the pole. Furthermore, there is no number θ for which r = 0 , so the graph does not pass through the pole. Observe that r is positive for all θ , r increases as θ increases, r → 0 as θ → − ∞ . Let’s find the values from 0 to 2 π to get single line spiral. θ r = 3 θ 0 2 0 = 1 π 6 2 ( π 6 ) = 1 . 7 8 π 3 3 ( π 3 ) = 3 . 1 6 π 2 3 ( π 2 ) = 5 . 6 2 2 π 3 3 ( 2 π 3 ) = 9 ...

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ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 9.2, Problem 58AYU

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Chapter 9.2, Problem 57AYU

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

Solution Summary: The author analyzes how the graph of r = 3 is an equation of spiral.

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Chapter 9 Solutions

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

Solution Summary: The author analyzes how the graph of r = 3 is an equation of spiral.

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

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Chapter 9 Solutions

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To find: Identify the polar equation $r = 3^{θ}$ and graph it.