Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 395: 56

Answer

$r = 6-3~cos~\theta$ This graph is a limacon. We can see this graph below:

Work Step by Step

$r = 6-3~cos~\theta$ When $\theta = 0^{\circ}$, then $r = 6-3~cos~0^{\circ} = 3$ When $\theta = 30^{\circ}$, then $r = 6-3~cos~30^{\circ} = 3.4$ When $\theta = 60^{\circ}$, then $r = 6-3~cos~60^{\circ} = 4.5$ When $\theta = 90^{\circ}$, then $r = 6-3~cos~90^{\circ} = 6$ When $\theta = 120^{\circ}$, then $r = 6-3~cos~120^{\circ} = 7.5$ When $\theta = 180^{\circ}$, then $r = 6-3~cos~180^{\circ} = 9$ When $\theta = 240^{\circ}$, then $r = 6-3~cos~240^{\circ} = 7.5$ When $\theta = 270^{\circ}$, then $r = 6-3~cos~270^{\circ} = 6$ When $\theta = 300^{\circ}$, then $r = 6-3~cos~300^{\circ} = 4.5$ When $\theta = 330^{\circ}$, then $r = 6-3~cos~330^{\circ} = 3.4$ This graph is a limacon. We can see this graph below:
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