Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 743: 80


$$y=\sqrt{3}x-16 \\ m=\sqrt{3}, \qquad b=-16$$

Work Step by Step

We find the line as follows: $$r \cos \left ( \theta + \frac{\pi }{6} \right )=8 \quad \Rightarrow \quad r \left ( \cos \theta \cos \frac{\pi }{6} - \sin \theta \sin \frac{\pi }{6} \right )=8 \quad \Rightarrow \quad \frac{\sqrt{3}}{2}r\cos \theta - \frac{1}{2} r \sin \theta =8 \quad \Rightarrow \quad \frac{\sqrt{3}}{2}x-\frac{1}{2}y=8 \quad \Rightarrow \quad y=\sqrt{3}x-16$$This line has slope $m=\sqrt{3}$ and $y$-intercept $b=-16$.
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