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Let U = {(u, v) : 0 < u < 27, v € R} and o : U → R³ be defined by o(u, v) = (cos u, sin u, v). a) Show that o is a regular surface patch and describe o(U). b) Let U = {(u, v) : - < u < 7, v E R} and let ở : Ũ → R be defined by a(u, v) = (cos u, sin u, v). Describe ở(U) and deduce that these two

Let U = {(u, v) : 0 < u < 27, v € R} and o : U → R³ be defined by o(u, v) = (cos u, sin u, v). a) Show that o is a regular surface patch and describe o(U). b) Let U = {(u, v) : - < u < 7, v E R} and let ở : Ũ → R be defined by a(u, v) = (cos u, sin u, v). Describe ở(U) and deduce that these two

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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1:42 M Y & B all 79% i You 2 minutes ago Let U = {(u, v) : 0 < u < 27, v E R} and o : U → R³ be defined by o(u, v) = (cos u, sin u, v). a) Show that o is a regular surface patch and describe o(U). b) Let U = {(u, v) : –x < u < T, v € R} and let ở : Ū → R³ be defined by ō(u, v) = (cos u, sin u, v). Describe ō(Ū) and deduce that these two surface patches form a smooth atlas of the unit cylinder r² + y² = 1. c) Find the transition map of the previous atlas and precise its domain and range.
Transcribed Image Text:1:42 M Y & B all 79% i You 2 minutes ago Let U = {(u, v) : 0 < u < 27, v E R} and o : U → R³ be defined by o(u, v) = (cos u, sin u, v). a) Show that o is a regular surface patch and describe o(U). b) Let U = {(u, v) : –x < u < T, v € R} and let ở : Ū → R³ be defined by ō(u, v) = (cos u, sin u, v). Describe ō(Ū) and deduce that these two surface patches form a smooth atlas of the unit cylinder r² + y² = 1. c) Find the transition map of the previous atlas and precise its domain and range.
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