Explanation Given info: R < Cos θ , Sin θ > Concept used: N ( t ) = T ' ( t ) ‖ T ' ( t ) ‖ Calculation: r ( Q ) = R < Cos θ , Sin θ > Differentiate with respect to Q , you get r ' ( Q ) = R < − Sin θ , Cos θ > Again double differentiate with respect to Q , you get r ' ' ( Q ) = R < − Cos θ , − Sin θ > Now, Magnitude of r ' ( Q ) can be find out | r ' ( Q ) | = R Sin 2 θ + Cos 2 θ = R Now, Tangent vector = T ( t ) = r ' ( t ) ‖ r ' ( t ) ‖ T ( Q ) = R < − Sin θ , Cos θ > R = < − Sin θ , Cos θ Differentiating with respect to Q T ' ( Q ) = < − Cos θ , − Sin θ >

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 14.4, Problem 37E

To determine

Find the normal vector $N (Q) to r (Q) = R < \cos θ, \sin θ >$ , the circle of radius $R$ .Does

$N (Q)$ Point is inside or outside of the circle?

Draw $N (Q) at θ = \frac{π}{4} with R = 4$

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Chapter 14.4, Problem 36E

Chapter 14.4, Problem 38E

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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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Find the normal vector N ( Q ) to r ( Q ) = R < cos θ , sin θ > , the circle of radius R .Does N ( Q ) Point is inside or outside of the circle? Draw N ( Q ) at θ = π 4 with R = 4

Solution Summary: The author calculates the normal vector N (Q) to r (q) = R cos, sin, and the circle of radius R.

Concept explainers

Find the normal vector $N (Q) to r (Q) = R < \cos θ, \sin θ >$ , the circle of radius $R$ .Does

$N (Q)$ Point is inside or outside of the circle?

Draw $N (Q) at θ = \frac{π}{4} with R = 4$

Want to see the full answer?

Chapter 14 Solutions

Find the normal vector N ( Q ) to r ( Q ) = R &lt; cos θ , sin θ &gt; , the circle of radius R .Does N ( Q ) Point is inside or outside of the circle? Draw N ( Q ) at θ = π 4 with R = 4

Solution Summary: The author calculates the normal vector N (Q) to r (q) = R cos, sin, and the circle of radius R.

Concept explainers

Find the normal vector N(Q) to r(Q)=R<cosθ,sinθ>, the circle of radius R.Does N(Q) Point is inside or outside of the circle? Draw N(Q) at θ=π4 with R = 4

Want to see the full answer?

Chapter 14 Solutions

Find the normal vector N ( Q ) to r ( Q ) = R < cos θ , sin θ > , the circle of radius R .Does N ( Q ) Point is inside or outside of the circle? Draw N ( Q ) at θ = π 4 with R = 4

Find the normal vector $N (Q) to r (Q) = R < \cos θ, \sin θ >$ , the circle of radius $R$ .Does

$N (Q)$ Point is inside or outside of the circle?

Draw $N (Q) at θ = \frac{π}{4} with R = 4$