Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.4 Vectors - 8.4 Assess Your Understanding - Page 627: 68



Work Step by Step

Let us consider that a vector $v$ is given by $v=pi+qj$ and makes an angle of $\alpha$ with the positive $x$-axis. The direction angle $\alpha$ for the given vector can be determined using the formula: $\tan \alpha=\dfrac{q}{p}$ Here, we have: $v=6 i - 4j $ Now, $\tan \alpha=\dfrac{ -4}{6}=\dfrac{-2}{3}$ Since the angle must be in the quadrant IV, the direction angle is: $\alpha=\arctan (\dfrac{-2}{3})=326.30^{\circ}$
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