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 ) ...

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

See similar textbooks

Concept explainers

Statements and Logic

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

Videos

Question

Chapter 14.4, Problem 48E

To determine

To calculate:

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

$〈 t - \sin t, 1 - \cos t 〉, t = π$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 47E

Chapter 14.4, Problem 49E

Students have asked these similar questions

Find the tangent line approximation 7 to the graph of f at the given point. T(x) = f(x) = csc(x), (8, csc(8)) Complete the table. (Round your answers to four decimal places.) x f(x) T(x) 7.9 7.99 8 8.01 8.1

Can you solve it numerical method

Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) Function x-Value Differential of x Ду = dy = y = x² + 2 x = -4 Ax = dx = 0.01

Chapter 14 Solutions

EBK CALCULUS

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

$〈 t - \sin t, 1 - \cos t 〉, t = π$