a. Explanation Given information: The circle is r = a cos θ . Formula used : tan α = f ( θ ) f ' ( θ ) , f ' ( θ ) ≠ 0 Calculation: The circle is r = a cos θ . Let f ( θ ) = a cos θ Differentiating f ( θ ) with respect to ‘ θ ’, we get f ' ( θ ) = − a sin θ b. To determine To find : tan α for the cardioid r = 2 ( 1 − cos θ ) c. To determine To find : tan α for the logarithmic spiral r = 2 e 3 θ

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.3, Problem 59PS

To determine

To find: tanα for the circle r=acosθ

To determine

To find: tanα for the cardioid r=2(1−cosθ)

To determine

To find: tanα for the logarithmic spiral r=2e3θ

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Chapter 6.3, Problem 58PS

Chapter 6.3, Problem 60PS

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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tan α for the circle r = a cos θ

Solution Summary: The author calculates mathrmtanalpha for the circle.

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To find: tanα for the circle r=acosθ

To find: tanα for the cardioid r=2(1−cosθ)

To find: tanα for the logarithmic spiral r=2e3θ

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Chapter 6 Solutions