Explanation Given: Curve = r ( t ) = 〈 4 , sin 2 t , cos 2 t 〉 Formula used: Tangent vector = T(t) = r ' ( t ) | | r ' ( t ) | | Normal vector = N(t) = T ' ( t ) | | T ' ( t ) | | Calculation: First we need to find tangent vector before finding normal vector. Tangent vector = T(t) = r ' ( t ) | | r ' ( t ) | | Now, r ' ( t ) = 〈 0 , 2 cos 2 t , − 2 sin 2 t 〉 ⇒ | | r ' ( t ) | | = ( 2 cos 2 t ) 2 + ( − 2 sin 2 t ) 2 = 4 cos 2 2 t + 4 sin 2 2 t = 4 ( cos 2 2 t + sin 2 2 t ) = 4 ( 1 ) = 2 ∴ T(t) = r ' ( t ) | | r ' ( t ) | | = 〈 0 , 2 cos

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Author: Rogawski

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Chapter 13.4, Problem 37E

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The normal vectorto the curve 〈4,sin2t,cos2t〉.

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Chapter 13.4, Problem 36E

Chapter 13.4, Problem 38E

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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 vectorto the curve 〈 4 , sin 2 t , cos 2 t 〉 .

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The normal vectorto the curve 〈4,sin2t,cos2t〉.

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Chapter 13 Solutions