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SOLUTION: A vector equation of the circular helix is R(t) = a cos ti + a sin tj + tk So D,R(t) =-a sin ti + a cos tj + k and |D,R(t)|= Va +1. From (3) we get T(t) = Vat + (-a sin ti + a cos tj + k) NSIONAL SPACE AND SOLID ANALYTIC GEOMETRY So D,T(t) = VI (-a cos ti – a sin tj) Applying (8), we obtain K(t) a² +1 (-a cos ti -- a sin tj) The curvature, then, is given by K(t) = |K(t)| = and so the curvature of the circular helix is constant. From (11) we get N(t) =-cos ti – sin tj Applying (12), we have B() = VT (-a sin ti + a cos tj + k) × (-cos ti – sin tj) Va? +1 1 Va + 1 (sin ti – cos tj + ak) - COS

SOLUTION: A vector equation of the circular helix is R(t) = a cos ti + a sin tj + tk So D,R(t) =-a sin ti + a cos tj + k and |D,R(t)|= Va +1. From (3) we get T(t) = Vat + (-a sin ti + a cos tj + k) NSIONAL SPACE AND SOLID ANALYTIC GEOMETRY So D,T(t) = VI (-a cos ti – a sin tj) Applying (8), we obtain K(t) a² +1 (-a cos ti -- a sin tj) The curvature, then, is given by K(t) = |K(t)| = and so the curvature of the circular helix is constant. From (11) we get N(t) =-cos ti – sin tj Applying (12), we have B() = VT (-a sin ti + a cos tj + k) × (-cos ti – sin tj) Va? +1 1 Va + 1 (sin ti – cos tj + ak) - COS

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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SOLUTION: A vector equation of the circular helix is R(t) = a cos ti + a sin tj + tk So D,R(t) =-a sin ti + a cos tj + k and |D,R(t)|= Va +1. From (3) we get T(t) = Vat + (-a sin ti + a cos tj + k) NSIONAL SPACE AND SOLID ANALYTIC GEOMETRY So D,T(t) = VI (-a cos ti – a sin tj) Applying (8), we obtain K(t) a² +1 (-a cos ti -- a sin tj) The curvature, then, is given by K(t) = |K(t)| = and so the curvature of the circular helix is constant. From (11) we get N(t) =-cos ti – sin tj Applying (12), we have B() = VT (-a sin ti + a cos tj + k) × (-cos ti – sin tj) Va? +1 1 Va + 1 (sin ti – cos tj + ak) - COS
Transcribed Image Text:SOLUTION: A vector equation of the circular helix is R(t) = a cos ti + a sin tj + tk So D,R(t) =-a sin ti + a cos tj + k and |D,R(t)|= Va +1. From (3) we get T(t) = Vat + (-a sin ti + a cos tj + k) NSIONAL SPACE AND SOLID ANALYTIC GEOMETRY So D,T(t) = VI (-a cos ti – a sin tj) Applying (8), we obtain K(t) a² +1 (-a cos ti -- a sin tj) The curvature, then, is given by K(t) = |K(t)| = and so the curvature of the circular helix is constant. From (11) we get N(t) =-cos ti – sin tj Applying (12), we have B() = VT (-a sin ti + a cos tj + k) × (-cos ti – sin tj) Va? +1 1 Va + 1 (sin ti – cos tj + ak) - COS
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