Explanation Given info. r → ( t ) = 〈 t − sin t , 1 − cos t 〉 Formula used: N → ( t ) = v ( t ) r ' ' ( t ) − v ' ( t ) r ' ( t ) ‖ v ( t ) r ' ' ( t ) − v ' ( t ) r ' ( t ) ‖ r → ' ( t ) = d r → ( t ) d t v ( t ) = ‖ r → ' ( t ) ‖ r ' ' ( t ) = d 2 r → ( t ) d t 2 v ' ( t ) = d d t v → ( t ) Calculation: r → ( t ) = 〈 t − sin t , 1 − cos t 〉 ⋯ ⋯ ( 1 ) r → ′ ( t ) = d d t r → ( t ) = d d t 〈 t − sin t , 1 − cos t 〉 = 〈 d d t ( t − sin t ) , d d t ( 1 − cos t ) 〉 = 〈 1 − cos t , sin t 〉 ⋯ ⋯ ( 2 ) V ( t ) = ‖ r → ' ( t ) ‖ = ( 1 − cos t ) 2 + ( sin t ) 2 = 1 + cos 2 t − 2 cos t + sin 2 t = 1 + 1 − 2 cos t = 2 − 2 cos t = 2 ( 1 − cos t ) = 2 × 2 sin 2 t 2 = 2 sin t 2 ⋯ ⋯ ( 3 ) r " ( t ) = d d t r → ' ( t ) = d d t 〈 1 − cos t , sin t 〉 = 〈 d d t ( 1 − cos t ) , d d t sin t 〉 = 〈 sin t , cos t 〉 ⋯ ⋯ ( 4 ) V ' ( t ) = 2 cos t 2 × 1 2 = cos t 2 ⋯ ⋯ ( 5 ) Substitute t = π in the equation ( 2 ) , ( 3 ) , ( 4 ) and ( 5 ) ...

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 14.4, Problem 48E

To determine

To calculate:

Normal vector $(\vec{N})$ at the point indicated.

$〈 t - \sin t, 1 - \cos t 〉, t = π$

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Chapter 14.4, Problem 47E

Chapter 14.4, Problem 49E

Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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Normal vector ( N → ) at the point indicated. 〈 t − sin t , 1 − cos t 〉 , t = π

Solution Summary: The author calculates a normal vector ( N ) at the point indicated.

Concept explainers

Videos

To calculate:

Normal vector $(\vec{N})$ at the point indicated.

$〈 t - \sin t, 1 - \cos t 〉, t = π$

Want to see the full answer?

Chapter 14 Solutions

Normal vector ( N → ) at the point indicated. 〈 t − sin t , 1 − cos t 〉 , t = π

Solution Summary: The author calculates a normal vector ( N ) at the point indicated.

Concept explainers

Videos

To calculate: Normal vector (N→) at the point indicated. 〈t−sint,1−cost〉,t=π

Want to see the full answer?

Chapter 14 Solutions

To calculate:

Normal vector $(\vec{N})$ at the point indicated.

$〈 t - \sin t, 1 - \cos t 〉, t = π$