1) Consider the spiral r:-7, 7 R' defined by (cos(s) r(s) sin(s). i) Compute the unit tangent vector t(s) – r'(s)/|P(s)| ii) Compute the normal n(s) ii) Compute b(s) = t(s) × n(s). iv) State the Cartesian equation of the plane which passes throu r(s) and has normal b(s) (this is called the "oseulating plane" which literally means the plane that kisses the eurve, so called because this plane has maximum contact with the curve). v) The coeflicient 7 such that b'(s) curve (geometrically, this coeflicient measures how the eurve twists throngh space). State the torsion of the spiral. ) For a general curve r: / R, define the vectors t(s), n(s) and b(s) as l'(s)/||t(s)||- TH(s) is called the torsion of the t'(s) t(s) ,n(s) and b(s) t(s) x n(s), You may assume r'(s)|| and ||t'(N)|| are non

1) Consider the spiral r:-7, 7 R' defined by (cos(s) r(s) sin(s). i) Compute the unit tangent vector t(s) – r'(s)/|P(s)| ii) Compute the normal n(s) ii) Compute b(s) = t(s) × n(s). iv) State the Cartesian equation of the plane which passes throu r(s) and has normal b(s) (this is called the "oseulating plane" which literally means the plane that kisses the eurve, so called because this plane has maximum contact with the curve). v) The coeflicient 7 such that b'(s) curve (geometrically, this coeflicient measures how the eurve twists throngh space). State the torsion of the spiral. ) For a general curve r: / R, define the vectors t(s), n(s) and b(s) as l'(s)/||t(s)||- TH(s) is called the torsion of the t'(s) t(s) ,n(s) and b(s) t(s) x n(s), You may assume r'(s)|| and ||t'(N)|| are non

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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