Explanation Given info. r → 1 ( t ) = ( cos t , sin t ) r → 2 ( t ) = ( sin t , cos t ) Concept used: Calculation: r → 1 ( t ) = ( cos t , sin t ) for t = 0 r → 1 ( 0 ) = ( 1 , 0 ) Let P 1 = ( 1 , 0 ) for t = π 2 r → 1 ( π 2 ) = ( cos π 2 , sin π 2 ) = ( 0 , 1 ) Let ( 0 , 1 ) r → 1 ( π ) = ( cos π , sin π ) = ( − 1 , 0 ) Let P 3 = ( − 1 , 0 ) Plotting these point on coordinate system and connect from p 1 , p 2 , p 3 are of unit circle. Hence this represents a circle of unit radius with center ( 0 , 0 ) , as t increases from 0 to 2 π , curve will trace in anti-clock wise...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 14.1, Problem 5PQ

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How do the paths ${\vec{r}}_{1} (t) = (\cos t, \sin t)$ and ${\vec{r}}_{2} (t) = (\sin t, \cos t)$ around the unit circle differ?

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Chapter 14.1, Problem 4PQ

Chapter 14.1, Problem 6PQ

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Chapter 14 Solutions

Calculus - Standalone book

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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How do the paths r → 1 ( t ) = ( cos t , sin t ) and r → 2 ( t ) = ( sin t , cos t ) around the unit circle differ?

Solution Summary: The author explains how the paths r 1 (t) = ( cos t, sin

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How do the paths ${\vec{r}}_{1} (t) = (\cos t, \sin t)$ and ${\vec{r}}_{2} (t) = (\sin t, \cos t)$ around the unit circle differ?

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Chapter 14 Solutions

How do the paths r → 1 ( t ) = ( cos t , sin t ) and r → 2 ( t ) = ( sin t , cos t ) around the unit circle differ?

Solution Summary: The author explains how the paths r 1 (t) = ( cos t, sin

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How do the paths r→1(t)=(cost,sint) and r→2(t)=(sint,cost) around the unit circle differ?

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Chapter 14 Solutions

How do the paths ${\vec{r}}_{1} (t) = (\cos t, \sin t)$ and ${\vec{r}}_{2} (t) = (\sin t, \cos t)$ around the unit circle differ?