Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.5 Harmonic Motion - 4.5 Exercises - Page 186: 17b


Period$=\frac{1}{2}$ seconds. Frequency=2 cycles per second.

Work Step by Step

The period can be found by first comparing the equation $s(t)=-5\cos 4\pi t$ to $s(t)=a\cos w t$ to find $w$ which is the angular velocity. By comparing the two equations, we find that $w=4\pi$. Next, we find the period using the formula: Period$=\frac{2\pi}{w}$ Period$=\frac{2\pi}{4\pi}$ Period$=\frac{1}{2}$ seconds. Since frequency is the reciprocal of the period, the frequency is 2 cycles per second.
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