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: 66

Answer

$225^{\circ}$

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=-5 i -5 j $ Now, $\tan \alpha=\dfrac{ -5}{-5}=1$ Which gives $\alpha=45^{\circ}$. Since the angle must be in the 3rd quadrant, then the direction angle is: $\alpha=\arctan (1)=225^{\circ}$
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