A cycloid A cycloid is the path traced by a point on a

Chapter 11, Problem 46E

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QUESTION:

A cycloid A cycloid is the path traced by a point on a rolling circle (think of a light on the rim of a moving bicycle wheel) The cycloid generated by a circle of radius a is given by the parametric equations

\(x=a(t-\sin t), \quad y=a(1-\cos t)\)

the parameter range \(0 \leq t \leq 2 \pi\) produces one arch of the cycloid (see figure). Show that the length of one arch of a cycloid is 8a.

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QUESTION:

A cycloid A cycloid is the path traced by a point on a rolling circle (think of a light on the rim of a moving bicycle wheel) The cycloid generated by a circle of radius a is given by the parametric equations

\(x=a(t-\sin t), \quad y=a(1-\cos t)\)

the parameter range \(0 \leq t \leq 2 \pi\) produces one arch of the cycloid (see figure). Show that the length of one arch of a cycloid is 8a.

ANSWER:

Solution 46EStep 1: Given that A cycloid is the path traced by a point on a circle rolling on a flat surface (think of a light on the rim of a moving bicycle wheel). The cycloid generated by a circle of radius a is given by the parametric equations x = a(t sin t), y = a(1cos t);the parameter range 0 t 2 produces one arch of the cycloid. Show that the length of one arch of a cycloid is 8a. 5.PNG

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