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: 37


$ \dfrac{5\pi}{12}$

Work Step by Step

We know that the angle between two vectors is: $\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$ Therefore, $u .v=\cos \dfrac{\pi}{3}\cos \dfrac{3\pi}{4}+\sin \dfrac{\pi}{3}\sin \dfrac{3\pi}{4} $ and $||u||=1$ and $||v||=1$ $\cos \theta = [\cos \dfrac{\pi}{3}\cos \dfrac{3\pi}{4}+\sin \dfrac{\pi}{3}\sin \dfrac{3\pi}{4} ]$ or, $= \cos ( \dfrac{\pi}{3}- \dfrac{3\pi}{4} )$ or, $= \cos (- \dfrac{5\pi}{12})$ So, $\theta = \dfrac{5\pi}{12}$
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