Trigonometry (11th Edition) Clone

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

Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 210: 102b


Write $P$ in terms of $\sin(2\pi t)$: $$P=16k-16k\sin^2(2\pi t)$$

Work Step by Step

From part a), we have the expression of $P$ $$P=16k\cos^2(2\pi t)$$ From Pythagorean Identity, we have $$\cos^2\theta=1-\sin^2\theta$$ Therefore, similarly in $P$, $$P=16k[1-\sin^2(2\pi t)]$$ $$P=16k-16k\sin^2(2\pi t)$$
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