Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.4 - Sum and Difference Equations - 7.4 Exercises - Page 539: 80


$y_1+y_2=2A\cos (\dfrac{2\pi t}{T}) \cos (\dfrac{ 2\pi x}{\lambda})$

Work Step by Step

By using the Sum and Difference formulas: $\cos (a+b)=\cos a \cos b -\sin a \sin b$ and $\cos (a-b)=\cos a \cos b +\sin a \sin b$ $y_1+y_2=A[\cos 2\pi (\dfrac{t}{T} -\dfrac{x}{\lambda})+ \cos 2\pi(\dfrac{t}{T} -\dfrac{x}{\lambda})]$ Now, $y_1+y_2=A[\cos 2\pi (\dfrac{t}{T} -\dfrac{x}{\lambda})+ \cos 2\pi(\dfrac{t}{T} -\dfrac{x}{\lambda})]$ or, $y_1+y_2=2A\cos (\dfrac{2\pi t}{T}) \cos (\dfrac{ 2\pi x}{\lambda})$
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