Explanation Given: The equation of cylinder is x 2 + y 2 = r 2 and the plane has equation z = a x + b y . Calculation: The equation of cylinder is x 2 + y 2 = r 2 and the plane has equation z = a x + b y . We have to find the vector parametrization r ( t ) of the curve of intersection. Let x = r cos t and y = r sin t . x 2 + y 2 = r 2 cos 2 t + r 2 sin 2 t = r 2 ( cos 2 t + sin 2 t ) = r 2 Therefore, the surface x 2 + y 2 = r 2 has trigonometric parametrization. So, x = r cos t and y = r sin t ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.1, Problem 52E

To determine

Find the vector parametrization $r (t)$ of the curve of intersection using the trigonometric functions $y = \cos t and y = \sin t$ .

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Chapter 14.1, Problem 51E

Chapter 14.1, Problem 53E

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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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Find the vector parametrization r ( t ) of the curve of intersection using the trigonometric functions y = cos t and y = sin t .

Solution Summary: The author explains how to determine the vector parametrization r ( t ) of the curve of intersection using the trigonometric functions y = cos

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Find the vector parametrization $r (t)$ of the curve of intersection using the trigonometric functions $y = \cos t and y = \sin t$ .

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Chapter 14 Solutions

Find the vector parametrization r ( t ) of the curve of intersection using the trigonometric functions y = cos t and y = sin t .

Solution Summary: The author explains how to determine the vector parametrization r ( t ) of the curve of intersection using the trigonometric functions y = cos

Concept explainers

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Find the vector parametrization r(t) of the curve of intersection using the trigonometric functions y=cost and y=sint.

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Chapter 14 Solutions

Find the vector parametrization $r (t)$ of the curve of intersection using the trigonometric functions $y = \cos t and y = \sin t$ .