Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 389: 67

Answer

$r = \theta$

Work Step by Step

The red graph shows $r = \theta$ for values of $\theta$ such that $0 \leq \theta \leq \frac{20\pi}{3}$ The violet graph shows $r = \theta$ for values of $\theta$ such that $-\frac{20\pi}{3} \leq \theta \leq 0$ Note that $r = 0$ when $\theta = 0$, and the magnitude of $r$ continues to increase as the magnitude of $\theta$ increases. This leads to a spiral shape. There is symmetry in the graph about the vertical axis since we include both positive and negative values of $\theta$
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