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 Formulas - 7.4 Exercises - Page 540: 89


$a \sin \beta \theta+b \cos \beta \theta$

Work Step by Step

$\tan C=\dfrac{opposite}{adjacent}=\dfrac{b}{a}$ $hypotenuse =\sqrt {a^2+b^2}$ $\cos C=\dfrac{adjacent}{hypotenuse}=\dfrac{a}{\sqrt {a^2+b^2}}$ $\sin C=\dfrac{opposite}{hypotenuse}=\dfrac{b}{\sqrt {a^2+b^2}}$ Now, $\sqrt {a^2+b^2}(\sin \beta \theta \cos C +\cos \beta \theta \sin C) $ or, $\sqrt {a^2+b^2}[\sin \beta \theta (\dfrac{a}{\sqrt {a^2+b^2}}) +\cos \beta \theta (\dfrac{b}{\sqrt {a^2+b^2}})] $ or, $a \sin \beta \theta+b \cos \beta \theta$
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