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: 57

Answer

$r = 2~sin~\theta~tan~\theta$ This graph is a cissoid. We can see this graph below:

Work Step by Step

$r = 2~sin~\theta~tan~\theta$ When $\theta = 0^{\circ}$, then $r = 2~sin~0^{\circ}~tan~0^{\circ} = 0$ When $\theta = 30^{\circ}$, then $r = 2~sin~30^{\circ}~tan~30^{\circ} = 0.58$ When $\theta = 60^{\circ}$, then $r = 2~sin~60^{\circ}~tan~60^{\circ} = 3$ When $\theta = 75^{\circ}$, then $r = 2~sin~75^{\circ}~tan~75^{\circ} = 7.2$ When $\theta = 75^{\circ}$, then $r = 2~sin~85^{\circ}~tan~85^{\circ} = 22.8$ When $\theta = 90^{\circ}$, then $r = 2~sin~90^{\circ}~tan~90^{\circ} = undefined$ When $\theta = 120^{\circ}$, then $r = 2~sin~120^{\circ}~tan~120^{\circ} = -3$ When $\theta = 180^{\circ}$, then $r = 2~sin~180^{\circ}~tan~180^{\circ} = 0$ When $\theta = 240^{\circ}$, then $r = 2~sin~240^{\circ}~tan~240^{\circ} = -3$ When $\theta = 270^{\circ}$, then $r = 2~sin~270^{\circ}~tan~270^{\circ} = undefined$ When $\theta = 300^{\circ}$, then $r = 2~sin~300^{\circ}~tan~300^{\circ} = 3$ This graph is a cissoid. We can see this graph below:
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