Explanation Consider the given equation, r = 3 2 + cos θ . Note that a curve is symmetric with respect to the line θ = π 2 , if r , θ and − r , − θ have the same value; symmetric with respect to the polar axis, if r , θ and r , − θ have the same value; and symmetric with respect to the pole if r , θ and − r , θ have the same value. First, check if it is symmetric with respect to the line, θ = π 2 . Replace − θ for θ and − r for r in r = 3 2 + cos θ , and use cos − θ = − cos θ . − r = 3 2 + cos − θ − r = 3 2 + cos θ r = − 3 2 + cos θ ≠ 3 2 + cos θ Since, r , θ ≠ − r , − θ , therefore curve is not symmetric with respect to the line, θ = π 2

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ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.8, Problem 16E

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Whether the polar equation, r=32+cosθ, is symmetric with respect to the line θ=π2, the polar axis and the pole.

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Chapter 6.8, Problem 15E

Chapter 6.8, Problem 17E

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Chapter 6 Solutions

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Whether the polar equation, r = 3 2 + cos θ , is symmetric with respect to the line θ = π 2 , the polar axis and the pole.

Solution Summary: The author explains that the polar equation, r=32+mathrmcostheta , is symmetric with respect to the line, axis

Whether the polar equation, r=32+cosθ, is symmetric with respect to the line θ=π2, the polar axis and the pole.

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Chapter 6 Solutions