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 390: 71a

Answer

$(r,-\theta)$

Work Step by Step

The polar graphs in this section exhibit symmetry. Visualize an xy-plane superimposed on the polar coordinate system, with the pole at the origin and the polar axis on the positive x-axis. Then a polar graph may be symmetric with respect to the x-axis (the polar axis), the y-axis( the line $\theta=\frac{\pi}{2}$) , or the origin (the pole). Since, the missing ordered pair is reflection to angle $\theta$ which is $-\theta$. Hence the desired result will be $(r,-\theta)$.
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