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: 52

Answer

$r = 3~cos~5\theta$ This graph is a rose. We can see this graph below:
1555681131

Work Step by Step

$r = 3~cos~5\theta$ When $\theta = 0^{\circ}$, then $r = 3~cos~0^{\circ} = 3$ When $\theta = 6^{\circ}$, then $r = 3~cos~30^{\circ} = 2.60$ When $\theta = 9^{\circ}$, then $r = 3~cos~45^{\circ} = 2.12$ When $\theta = 12^{\circ}$, then $r = 3~cos~60^{\circ} = 1.5$ When $\theta = 18^{\circ}$, then $r = 3~cos~90^{\circ} = 0$ When $\theta = 30^{\circ}$, then $r = 3~cos~150^{\circ} = -2.60$ When $\theta = 36^{\circ}$, then $r = 3~cos~180^{\circ} = -3$ When $\theta = 48^{\circ}$, then $r = 3~cos~240^{\circ} = -1.5$ When $\theta = 54^{\circ}$, then $r = 3~cos~270^{\circ} = 0$ When $\theta = 60^{\circ}$, then $r = 3~cos~300^{\circ} = 1.5$ When $\theta = 72^{\circ}$, then $r = 3~cos~360^{\circ} = 3$ When $\theta = 90^{\circ}$, then $r = 3~cos~450^{\circ} = 0$ When $\theta = 108^{\circ}$, then $r = 3~cos~540^{\circ} = -3$ When $\theta = 126^{\circ}$, then $r = 3~cos~630^{\circ} = 0$ When $\theta = 144^{\circ}$, then $r = 3~cos~720^{\circ} = 3$ When $\theta = 162^{\circ}$, then $r = 3~cos~810^{\circ} = 0$ When $\theta = 180^{\circ}$, then $r = 3~cos~900^{\circ} = -3$ For larger values of $\theta$, the points on the graph are repeated. This graph is a rose. We can see this graph below:
Small 1555681131
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