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An example of a phenomenon that repeats for a long time or "infinitely" long, is the spin of the earth, which has the period of $24\ hours$.
Precalculus (6th Edition) Blitzer
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13446-914-3
ISBN 13:
978-0-13446-914-0
Chapter 4 - Section 4.2 - Trigonometric Functions: The Unit Circle - Exercise Set - Page 549: 96
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