Explanation Given: Curve = r ( θ ) = R 〈 cos θ , sin θ 〉 = 〈 R cos θ , R sin θ 〉 Formula used: Tangent vector = T( θ ) = r ' ( θ ) | | r ' ( θ ) | | Normal vector = N( θ ) = T ' ( θ ) | | T ' ( θ ) | | Calculation: First we need to find tangent vector before finding normal vector. Tangent vector = T( θ ) = r ' ( θ ) | | r ' ( θ ) | | Now, r ' ( θ ) = 〈 − R sin θ , R cos θ 〉 ⇒ | | r ' ( θ ) | | = ( − R sin θ ) 2 + ( R cos θ ) 2 = R 2 sin 2 θ + R 2 cos 2 θ = R 2 ( sin 2 θ + cos 2 θ ) = R 2 ( 1 ) = R ∴ T( θ ) = r ' ( θ ) | | r ' ( θ ) | | = 〈 − R sin θ , R cos θ 〉 R = 〈 − sin θ , cos θ 〉 Normal vector = N( θ ) = T ' ( θ ) | | T ' ( θ ) | |

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ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 13.4, Problem 36E

To determine

The normal vector of curve r(θ)=R〈cosθ,sinθ〉 and draw it at when θ=π4 with R=4.

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Chapter 13.4, Problem 35E

Chapter 13.4, Problem 37E

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Chapter 13 Solutions

CALCULUS W/ACHIEVE PLATFORM

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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The normal vector of curve r ( θ ) = R 〈 cos θ , sin θ 〉 and draw it at when θ = π 4 with R = 4 .

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The normal vector of curve r(θ)=R〈cosθ,sinθ〉 and draw it at when θ=π4 with R=4.

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Chapter 13 Solutions