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Consider the spiral given by c(t) = (e2t cos(2t), e²t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let be the angle between c and c'. Using the dot product rule we have the following. c(t) c'(t) = ||c(t)||· ||c'(t)|| cos(0) 2e4t = This gives us cos(0) = and so 0 = cos(0) Therefore the angle between c and c' is constant.

Consider the spiral given by c(t) = (e2t cos(2t), e²t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let be the angle between c and c'. Using the dot product rule we have the following. c(t) c'(t) = ||c(t)||· ||c'(t)|| cos(0) 2e4t = This gives us cos(0) = and so 0 = cos(0) Therefore the angle between c and c' is constant.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the spiral given by c(t) = (e²t cos(2t), e²t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let be the angle between c and c'. Using the dot product rule we have the following. c(t) • c'(t) = ||c(t)||· ||c'(t)|| cos(0) 2e4t = This gives us cos(0) = and so 0 = cos(0) Therefore the angle between c and c' is constant.
Transcribed Image Text:Consider the spiral given by c(t) = (e²t cos(2t), e²t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let be the angle between c and c'. Using the dot product rule we have the following. c(t) • c'(t) = ||c(t)||· ||c'(t)|| cos(0) 2e4t = This gives us cos(0) = and so 0 = cos(0) Therefore the angle between c and c' is constant.
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