Trigonometry (11th Edition) Clone

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

Chapter 4 - Test - Page 194: 14c


Frequency$=4$ cycles Period$=\frac{1}{4}$ sec

Work Step by Step

We first write the equation in the form $y=a \cos [b(x-d)]$. Therefore, $y=-4\cos (8\pi t)$ becomes $y=0-4\cos [8\pi(t-0)]$. Comparing the two equations, $b=8\pi$. The period can be found from the formula: $\frac{2\pi}{b}$ Substituting the value of $b$ in this formula and solving: Period$=\frac{2\pi}{8\pi}$ Period$=\frac{1}{4}$ sec Since frequency=1/Period, Frequency$=\frac{1}{1/4}=4$ cycles
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