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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Only solve if you can answer parts with correct explanation otherwise skip it

Al. (a) Give an example of parametrised curve y : (0, 1) → R' which is
i. not regular; i. regular but not unit-speed; iii. regular and unit-speed.
(b) Assume that a unit-speed regular parametrised curve 3:(-7, 7) → R? with
Frenet frame (T, N) has constant curvature k > 0. Show that its tangent vector
T is of the form T(s) = cos(ks) a + sin(xs) b, for some a, b e R?.
Deduce that ||a||2 = 1, ||b|2 = 1, while a b 0. Furthermore, prove that 3 is
(part of) a circle of radius .
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