Answered: Change each equation to rectangular…

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section8.6: Equations In Polar Coordinates And Their Graphs

Problem 78PS

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Question

Change each equation to rectangular coordinates and then graph.

r(1 - cos u) = 1

Expert Solution

Given,

$r (1 - \cos θ) = 1 \Rightarrow r - r \cos θ = 1 \Rightarrow r = 1 + r \cos θ \Rightarrow \sqrt{x^{2} + y^{2}} = 1 + x [∵ x = r \cos θ & r = \sqrt{x^{2} + y^{2}}] \Rightarrow {(\sqrt{x^{2} + y^{2}})}^{2} = {(1 + x)}^{2} [Squaring on both sides] \Rightarrow x^{2} + y^{2} = 1 + 2 x + x^{2} \Rightarrow y^{2} = 2 x + 1$

Therefore rectangular equation is,

$y^{2} = 2 x + 1$

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