Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.5 Harmonic Motion - 4.5 Exercises - Page 180: 18b

Answer

Period$=\frac{\pi}{5}$ seconds Frequency=$\frac{5}{\pi}$ cycles per second

Work Step by Step

The period can be found by first comparing the equation $s(t)=-4\cos 10 t$ to $s(t)=a\cos w t$ to find $w$ which is the angular velocity. By comparing the two equations, we find that $w=10$. Next, we find the period using the formula: Period$=\frac{2\pi}{w}$ Period$=\frac{2\pi}{10}$ Period$=\frac{\pi}{5}$ seconds. Since frequency is the reciprocal of the period, the frequency is $\frac{5}{\pi}$ cycles per second.
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