Explanation Given: Curve = r ( t ) = 〈 t − sin t , 1 − cos t 〉 Formula used: Tangent vector = T(t) = r ' ( t ) | | r ' ( t ) | | 1 − cos t = 2 sin 2 t 2 sin t = 2 sin t 2 cos t 2 Calculation: r ( t ) = 〈 t − sin t , 1 − cos t 〉 Now, r ' ( t ) = 〈 1 − cos t , sin t 〉 ⇒ | | r ' ( t ) | | = ( 1 − cos t ) 2 + ( sin t ) 2 = 1 2 + cos 2 t − 2 cos t + sin 2 t [ ∵ ( a − b ) 2 = a 2 + b 2 − 2 a b ] = 1 − 2 cos t + ( sin 2 t + cos 2 t ) = 1 − 2 cos t + 1 = 2 − 2 cos t = 2 ( 1 − cos t ) [ ∵ 1 − cos t = 2 sin 2 t 2 ] = 2 × 2 sin

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 13.2, Problem 18E

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Find the values of t between 0 and 2π such that tangent vector to the cycloid r(t)=〈t−sint,1−cost〉 is a unit vector.

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Chapter 13.2, Problem 17E

Chapter 13.2, Problem 19E

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Find the values of t between 0 and 2 π such that tangent vector to the cycloid r ( t ) = 〈 t − sin t , 1 − cos t 〉 is a unit vector.

Solution Summary: The author explains how to find the values of t between 0 and 2pi such that tangent vector to the cycloid is a unit vector.

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Find the values of t between 0 and 2π such that tangent vector to the cycloid r(t)=〈t−sint,1−cost〉 is a unit vector.

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Chapter 13 Solutions