Explanation Formula Used: The arc length s , for a parametric curve c ( t ) = ( x ( t ) , y ( t ) ) is given by s ( t ) = ∫ 0 t [ x ′ ( t ) ] 2 + [ y ′ ( t ) ] 2 d t Calculations: Consider the parametric representation c ( θ ) = ( R ( cos θ + θ sin θ ) , R ( sin θ − θ cos θ ) ) Then, x ( θ ) = R ( cos θ + θ sin θ ) y ( θ ) = R ( sin θ − θ cos θ ) So, x ′ ( θ ) = R ( − sin θ + sin θ + θ cos θ ) = R θ cos θ y ′ ( θ ) = R ( cos θ − cos θ + θ sin θ ) = R θ sin θ Now, the arc length is evaluated as s ( θ ) =

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.2, Problem 29E

To determine

To find: the length of the curve C, for $0 \leq θ \leq 2 π$ , where C is parameterized by

$c (θ) = (R (\cos θ + θ \sin θ), R (\sin θ - θ \cos θ))$

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Chapter 12.2, Problem 28E

Chapter 12.2, Problem 30E

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the length of the curve C, for 0 ≤ θ ≤ 2 π , where C is parameterized by c ( θ ) = ( R ( cos θ + θ sin θ ) , R ( sin θ − θ cos θ ) )

Solution Summary: The author calculates the arc length for a parametric curve c ( t ) = 0 2.

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To find: the length of the curve C, for $0 \leq θ \leq 2 π$ , where C is parameterized by

$c (θ) = (R (\cos θ + θ \sin θ), R (\sin θ - θ \cos θ))$

Want to see the full answer?

Chapter 12 Solutions

the length of the curve C, for 0 ≤ θ ≤ 2 π , where C is parameterized by c ( θ ) = ( R ( cos θ + θ sin θ ) , R ( sin θ − θ cos θ ) )

Solution Summary: The author calculates the arc length for a parametric curve c ( t ) = 0 2.

Concept explainers

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To find: the length of the curve C, for 0≤θ≤2π, where C is parameterized by c(θ)=(R(cosθ+θsinθ),R(sinθ−θcosθ))

Want to see the full answer?

Chapter 12 Solutions

To find: the length of the curve C, for $0 \leq θ \leq 2 π$ , where C is parameterized by

$c (θ) = (R (\cos θ + θ \sin θ), R (\sin θ - θ \cos θ))$