Algebra and Trigonometry 10th Edition

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

Chapter 8 - 8.4 - Vectors and Dot Products - 8.4 Exercises - Page 595: 38



Work Step by Step

$\theta=cos^{-1}\frac{u\cdot v}{|u||v|}=cos^{-1}\frac{(cos(\frac{\pi}{4})i+sin(\frac{\pi}{4})j)(cos(\frac{5\pi}{4})i+sin(\frac{5\pi}{4})j)}{\sqrt {cos^2(\frac{\pi}{4})+sin^2(\frac{\pi}{4})}\sqrt {cos^2(\frac{5\pi}{4})+sin^2(\frac{5\pi}{4})}}=cos^{-1}\frac{cos(\frac{\pi}{4})~cos(\frac{5\pi}{4})+sin(\frac{\pi}{4})~sin(\frac{5\pi}{4})}{1}=cos^{-1}[cos(\frac{5\pi}{4}-\frac{\pi}{4})]=cos^{-1}[cos~\pi]=\pi$ Remember: $cos(a-b)=cos~a~cos~b+sin~a~sin~b$
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