Explanation Given info: Equation of circle in parametric form r → ( t ) = ( 6 + 3 Sin t , 9 , 4 + 3 Cos t ) Concept used: y − Co-ordinate on the circle does not change so it lies in the plane perpendicular to y − axis i .e a plane parallel to x z plane general equation of this type of circle is given as ( x − h ) = R Sin t y − k = 0 ( z − l ) = R Cos t , where ( h , k , l ) anther of circle R: radius of circle. Calculation: r → ( t ) = ( 6 + 3 Sin t , 9 , 4 + 3 Cos t ) Co-ordinate of points lie on circle is given by x = 6 + 3 Sin t y = 9 z = 4 + 3 Cos t Write above equation in standard format x − 6 = 3 Sin t y − 9 = 0 z − 4 = 3 Cos t Compare this standard format with ( x − h ) ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.1, Problem 22E

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The function $\vec{r} (t)$ traces a circle. Determine the radius, center and plane containing the circle. $\vec{r} (t) = (6 + 3 Sin t, 9, 4 + 3 Cos t)$ .

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Chapter 14.1, Problem 21E

Chapter 14.1, Problem 23E

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Chapter 14 Solutions

CALCULUS (CLOTH)

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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The function r → ( t ) traces a circle. Determine the radius, center and plane containing the circle. r → ( t ) = ( 6 + 3 Sin t , 9 , 4 + 3 Cos t ) .

Solution Summary: The author explains the function r ( t ) traces a circle. Determine the radius, center, and plane containing it.

Concept explainers

The function $\vec{r} (t)$ traces a circle. Determine the radius, center and plane containing the circle. $\vec{r} (t) = (6 + 3 Sin t, 9, 4 + 3 Cos t)$ .

Want to see the full answer?

Chapter 14 Solutions

The function r → ( t ) traces a circle. Determine the radius, center and plane containing the circle. r → ( t ) = ( 6 + 3 Sin t , 9 , 4 + 3 Cos t ) .

Solution Summary: The author explains the function r ( t ) traces a circle. Determine the radius, center, and plane containing it.

Concept explainers

The function r→(t) traces a circle. Determine the radius, center and plane containing the circle.r→(t)=(6+3Sint,9,4+3Cost).

Want to see the full answer?

Chapter 14 Solutions

The function $\vec{r} (t)$ traces a circle. Determine the radius, center and plane containing the circle. $\vec{r} (t) = (6 + 3 Sin t, 9, 4 + 3 Cos t)$ .