Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 9.5, Problem 36E

To determine

To calculate: To plot the point in rectangular coordinates and find two setsof polar representations of the point, using $0<θ<2π$

Expert Solution & Answer

Answer to Problem 36E

The rectangular coordinates of point on the graph is plotted and two sets of polar points are $(32,5π4),(−32,π4)$

Explanation of Solution

Given information: Rectangularis $(−3,−3)$

Formula Used:

Polar coordinate of a point $(x,y)$ is given as

$(r,θ)$

Where,

$r=x2+y2$

$θ=arctan(|yx|)$

If both $x,y>0$ , then $θ=α$

If $x<0,y>0$ , then $θ=π−α$

If $x,y<0$ , then $θ=π+α$

If $x>0,y<0$ , then $θ=−α$

Point $(r,θ)$ can be represented as

$(r,θ)=(r,θ±2nπ)$

$(r,θ)=(−r,θ±(2n+1)π)$

Calculation:

Rectangular point is given as

$(−3,−3)$

Plotting the rectangular coordinates on the graph

Precalculus with Limits: A Graphing Approach, Chapter 9.5, Problem 36E

Converting rectangular coordinates into polar coordinates:

Polar coordinate of a point $(x,y)$ is given as

$(r,θ)$

Calculating the value of $r$ :

$r=(−3)2+(−3)2r=9+9r=18r=32$

Calculating the value of $θ$ :

Since $x,y<0$ , then $θ=π+α$

$θ=πarctan(|−3−3|)θ=π+π4θ=5π4$

Thus, polar coordinate of point is $(32,5π4)$

Now, let’s find another set polar representations of the point, where $0<θ<2π$

Point $(r,θ)$ can be represented as

$(r,θ)=(−r,θ±(2n+1)π)$

Here,

$r=32θ=5π4$

Substituting the values in above representations, another representation of given point are:

$(−32,5π4−π)=(−32,π4)$

Conclusion:

Hence, rectangular coordinates of point on the graph is plotted and twosets of polar points are $(32,5π4),(−32,π4)$

Chapter 9.5, Problem 35E

Chapter 9.5, Problem 37E

Chapter 9 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - Prob. 71RE Ch. 9 - Prob. 72RE Ch. 9 - Prob. 73RE Ch. 9 - Prob. 74RE Ch. 9 - Prob. 75RE Ch. 9 - Prob. 76RE Ch. 9 - Prob. 77RE Ch. 9 - Prob. 78RE Ch. 9 - Prob. 79RE Ch. 9 - Prob. 80RE Ch. 9 - Prob. 81RE Ch. 9 - Prob. 82RE Ch. 9 - Prob. 83RE Ch. 9 - Prob. 84RE Ch. 9 - Prob. 85RE Ch. 9 - Prob. 86RE Ch. 9 - Prob. 87RE Ch. 9 - Prob. 88RE Ch. 9 - Prob. 89RE Ch. 9 - Prob. 90RE Ch. 9 - Prob. 91RE Ch. 9 - Prob. 92RE Ch. 9 - Prob. 93RE Ch. 9 - Prob. 94RE Ch. 9 - Prob. 95RE Ch. 9 - Prob. 96RE Ch. 9 - Prob. 97RE Ch. 9 - Prob. 98RE Ch. 9 - Prob. 99RE Ch. 9 - Prob. 100RE Ch. 9 - Prob. 101RE Ch. 9 - Prob. 102RE Ch. 9 - Prob. 103RE Ch. 9 - Prob. 104RE Ch. 9 - Prob. 105RE Ch. 9 - Prob. 106RE Ch. 9 - Prob. 107RE Ch. 9 - Prob. 108RE Ch. 9 - Prob. 109RE Ch. 9 - Prob. 110RE Ch. 9 - Prob. 111RE Ch. 9 - Prob. 112RE Ch. 9 - Prob. 113RE Ch. 9 - Prob. 114RE Ch. 9 - Prob. 115RE Ch. 9 - Prob. 116RE Ch. 9 - Prob. 117RE Ch. 9 - 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Prob. 38CLT Ch. 9 - Prob. 39CLT Ch. 9 - Prob. 40CLT Ch. 9 - Prob. 41CLT Ch. 9 - Prob. 42CLT Ch. 9 - Prob. 43CLT Ch. 9 - Prob. 44CLT Ch. 9 - Prob. 45CLT Ch. 9 - Prob. 46CLT Ch. 9 - Prob. 47CLT Ch. 9 - Prob. 48CLT Ch. 9 - Prob. 49CLT Ch. 9 - Prob. 50CLT Ch. 9 - Prob. 51CLT Ch. 9 - Prob. 52CLT Ch. 9 - Prob. 53CLT Ch. 9 - Prob. 54CLT Ch. 9 - Prob. 55CLT

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To plot the point in rectangular coordinates and find two setsof polar representations of the point, using 0 &lt; θ &lt; 2 π

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To calculate: To plot the point in rectangular coordinates and find two setsof polar representations of the point, using 0<θ<2π<m:math><m:mrow><m:mn>0</m:mn><m:mo>&lt;</m:mo><m:mi>θ</m:mi><m:mo>&lt;</m:mo><m:mn>2</m:mn><m:mi>π</m:mi></m:mrow></m:math>

Answer to Problem 36E

Explanation of Solution

Chapter 9 Solutions

To plot the point in rectangular coordinates and find two setsof polar representations of the point, using 0 < θ < 2 π

To calculate: To plot the point in rectangular coordinates and find two setsof polar representations of the point, using $0<θ<2π$