Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.6 - Vectors - Concept and Vocabulary Check - Page 781: 12


Let $\mathbf{v}$ be a nonzero vector. If $\theta $ is the direction angle measured from the positive x-axis to v, then the vector can be expressed in terms of its magnitude and direction angle as: $\mathbf{v}=\left\| \mathbf{v} \right\|\text{ }\underline{\cos \theta }\text{ }\mathbf{i}+\left\| \mathbf{v} \right\|\text{ }\underline{\sin \theta }\text{ }\mathbf{j}$

Work Step by Step

For representing any vector in the two systems of vectors, $\mathbf{i}$, and $\mathbf{j}$, which are mutually perpendicular with each other, we make an angle $\theta $ along the positive x-axis; then vector can be expressed by calculating three quantities: magnitude, $\cos \theta $, and $\sin \theta $, and it can be expressed as below: $\mathbf{v}=\left\| \mathbf{v} \right\|\text{ }\underline{\cos \theta }\text{ }\mathbf{i}+\left\| \mathbf{v} \right\|\text{ }\underline{\sin \theta }\text{ }\mathbf{j}$ Where $\left\| \mathbf{v} \right\|$ is the magnitude of vector $\mathbf{v}$.
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