Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
Question
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Chapter 9.6, Problem 21E
To determine

To calculate: To test for symmetry with respect to the line θ=π2 , the polar axis and the pole

Expert Solution & Answer
Check Mark

Answer to Problem 21E

The polar equation is NOT symmetric with respect to the line θ=π2 and polar axis, while equation is symmetric with respect to pole

Explanation of Solution

Given information: Polar equation is r2=16sin2θ

Formula Used:

Test for Symmetry:

To test symmetry with respect to the line θ=π2 , replace (r,θ) by (r,πθ)

To test symmetry with respect to the polar axis, replace (r,θ) by (r,θ)

To test symmetry with respect to the pole, replace (r,θ) by (r,π+θ)

Calculation:

Polar equation is given as follows:

  r2=16sin2θ

To test Symmetry respect with respect to the line θ=π2 :

Replacing (r,θ) by (r,πθ) , polar equation is

  r2=16sin2(πθ)r2=16sin(2π2θ)r2=16(sin2θ)r2=16sin2θ

Since above equation is NOT same as the given polar equation

Thus, polar equation is NOT symmetric with respect to the line θ=π2

To test Symmetry with respect to the polar axis

Replacing (r,θ) by (r,θ) , polar equation is

  r2=16sin2(θ)r2=16sin(2θ)r2=16(sin2θ)r2=16sin2θ

Since above equation is not same as the given polar equation

Thus, polar equation is NOT symmetric with respect to the polar axis

To test Symmetry with respect to the pole

Replacing (r,θ) by (r,π+θ) , polar equation is

  r2=16sin2(π+θ)r2=16sin(2π+2θ)r2=16(sin2θ)r2=16sin2θ

Since above equation is same as the given polar equation

Thus, polar equation is with respect to the pole

Conclusion:

Hence, polar equation is NOT symmetric with respect to the line θ=π2 and polar axis, while equation is symmetric with respect to pole

Chapter 9 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - 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Prob. 77ECh. 9.7 - Prob. 78ECh. 9.7 - Prob. 79ECh. 9.7 - Prob. 80ECh. 9.7 - Prob. 81ECh. 9.7 - Prob. 82ECh. 9.7 - Prob. 83ECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Prob. 64RECh. 9 - Prob. 65RECh. 9 - Prob. 66RECh. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 70RECh. 9 - Prob. 71RECh. 9 - Prob. 72RECh. 9 - Prob. 73RECh. 9 - Prob. 74RECh. 9 - Prob. 75RECh. 9 - Prob. 76RECh. 9 - Prob. 77RECh. 9 - Prob. 78RECh. 9 - Prob. 79RECh. 9 - Prob. 80RECh. 9 - Prob. 81RECh. 9 - Prob. 82RECh. 9 - Prob. 83RECh. 9 - Prob. 84RECh. 9 - Prob. 85RECh. 9 - Prob. 86RECh. 9 - Prob. 87RECh. 9 - Prob. 88RECh. 9 - Prob. 89RECh. 9 - Prob. 90RECh. 9 - Prob. 91RECh. 9 - Prob. 92RECh. 9 - Prob. 93RECh. 9 - Prob. 94RECh. 9 - Prob. 95RECh. 9 - Prob. 96RECh. 9 - Prob. 97RECh. 9 - Prob. 98RECh. 9 - Prob. 99RECh. 9 - Prob. 100RECh. 9 - Prob. 101RECh. 9 - Prob. 102RECh. 9 - Prob. 103RECh. 9 - Prob. 104RECh. 9 - Prob. 105RECh. 9 - Prob. 106RECh. 9 - Prob. 107RECh. 9 - Prob. 108RECh. 9 - Prob. 109RECh. 9 - Prob. 110RECh. 9 - Prob. 111RECh. 9 - Prob. 112RECh. 9 - Prob. 113RECh. 9 - Prob. 114RECh. 9 - Prob. 115RECh. 9 - Prob. 116RECh. 9 - Prob. 117RECh. 9 - Prob. 118RECh. 9 - Prob. 119RECh. 9 - Prob. 120RECh. 9 - Prob. 121RECh. 9 - Prob. 122RECh. 9 - Prob. 123RECh. 9 - Prob. 124RECh. 9 - Prob. 125RECh. 9 - Prob. 126RECh. 9 - Prob. 127RECh. 9 - Prob. 128RECh. 9 - Prob. 129RECh. 9 - Prob. 130RECh. 9 - Prob. 131RECh. 9 - Prob. 132RECh. 9 - Prob. 133RECh. 9 - Prob. 134RECh. 9 - Prob. 135RECh. 9 - Prob. 136RECh. 9 - Prob. 137RECh. 9 - Prob. 138RECh. 9 - Prob. 139RECh. 9 - Prob. 140RECh. 9 - Prob. 141RECh. 9 - Prob. 142RECh. 9 - Prob. 143RECh. 9 - Prob. 144RECh. 9 - Prob. 145RECh. 9 - Prob. 146RECh. 9 - Prob. 147RECh. 9 - Prob. 148RECh. 9 - Prob. 149RECh. 9 - Prob. 150RECh. 9 - Prob. 151RECh. 9 - Prob. 152RECh. 9 - Prob. 153RECh. 9 - Prob. 154RECh. 9 - Prob. 155RECh. 9 - Prob. 156RECh. 9 - Prob. 157RECh. 9 - Prob. 158RECh. 9 - Prob. 1CTCh. 9 - Prob. 2CTCh. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - Prob. 8CTCh. 9 - Prob. 9CTCh. 9 - Prob. 10CTCh. 9 - Prob. 11CTCh. 9 - Prob. 12CTCh. 9 - Prob. 13CTCh. 9 - Prob. 14CTCh. 9 - Prob. 15CTCh. 9 - Prob. 16CTCh. 9 - Prob. 17CTCh. 9 - Prob. 18CTCh. 9 - Prob. 19CTCh. 9 - Prob. 20CTCh. 9 - Prob. 21CTCh. 9 - Prob. 22CTCh. 9 - Prob. 23CTCh. 9 - Prob. 24CTCh. 9 - Prob. 25CTCh. 9 - Prob. 1CLTCh. 9 - Prob. 2CLTCh. 9 - Prob. 3CLTCh. 9 - Prob. 4CLTCh. 9 - Prob. 5CLTCh. 9 - Prob. 6CLTCh. 9 - Prob. 7CLTCh. 9 - Prob. 8CLTCh. 9 - Prob. 9CLTCh. 9 - Prob. 10CLTCh. 9 - Prob. 11CLTCh. 9 - Prob. 12CLTCh. 9 - Prob. 13CLTCh. 9 - Prob. 14CLTCh. 9 - Prob. 15CLTCh. 9 - Prob. 16CLTCh. 9 - Prob. 17CLTCh. 9 - Prob. 18CLTCh. 9 - Prob. 19CLTCh. 9 - Prob. 20CLTCh. 9 - Prob. 21CLTCh. 9 - Prob. 22CLTCh. 9 - Prob. 23CLTCh. 9 - Prob. 24CLTCh. 9 - Prob. 25CLTCh. 9 - Prob. 26CLTCh. 9 - Prob. 27CLTCh. 9 - Prob. 28CLTCh. 9 - Prob. 29CLTCh. 9 - Prob. 30CLTCh. 9 - Prob. 31CLTCh. 9 - Prob. 32CLTCh. 9 - Prob. 33CLTCh. 9 - Prob. 34CLTCh. 9 - Prob. 35CLTCh. 9 - Prob. 36CLTCh. 9 - Prob. 37CLTCh. 9 - Prob. 38CLTCh. 9 - Prob. 39CLTCh. 9 - Prob. 40CLTCh. 9 - Prob. 41CLTCh. 9 - Prob. 42CLTCh. 9 - Prob. 43CLTCh. 9 - Prob. 44CLTCh. 9 - Prob. 45CLTCh. 9 - Prob. 46CLTCh. 9 - Prob. 47CLTCh. 9 - Prob. 48CLTCh. 9 - Prob. 49CLTCh. 9 - Prob. 50CLTCh. 9 - Prob. 51CLTCh. 9 - Prob. 52CLTCh. 9 - Prob. 53CLTCh. 9 - Prob. 54CLTCh. 9 - Prob. 55CLT
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