Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) = r0 - r sin (0), y(0)=r -r cos(0).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 17EQ
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The practice problem is described in the picture attached.

Show that 8r units is the length, L, of one arch of the cycloid described
parametrically by:
x (0) = r0 - r sin (0), y(0)=r -r cos(0).
-2n
Hint: Note that 2 sin? (-) = 1– cos 0 and that
L = S" Jx'(0)² + y'(0)² d®.
Transcribed Image Text:Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) = r0 - r sin (0), y(0)=r -r cos(0). -2n Hint: Note that 2 sin? (-) = 1– cos 0 and that L = S" Jx'(0)² + y'(0)² d®.
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