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 394: 15

Answer

$(-2, 135^{\circ})$ (a) We can see the point plotted on the graph below. (b) We can write two other pairs of polar coordinates for this point: $(2, 315^{\circ})$ $(-2, -225^{\circ})$ (c) $(x,y) = (\sqrt{2},-\sqrt{2})$
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Work Step by Step

$(-2, 135^{\circ})$ (a) We can see the point plotted on the graph below. (b) We can write two other pairs of polar coordinates for this point: $(2, 315^{\circ})$ $(-2, -225^{\circ})$ (c) We can find the rectangular coordinates: $r = 2$ and $\theta = 315^{\circ}$ $(x,y) = (r~cos~\theta, r~sin~\theta)$ $(x,y) = (2~cos~315^{\circ}, 2~sin~315^{\circ})$ $(x,y) = (\sqrt{2},-\sqrt{2})$
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