Book edition 2nd

Author(s) James Stewart

Pages 830 pages

ISBN 9781133112280

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Short Answer

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with \(r > 0\)and one with \(r < 0\).
\(\begin{aligned}{l}(a)(1,7\pi /4)\\(b)( - 3,\pi /6)\\(c)(1, - 1)\end{aligned}\)

The other two coordinates are\((1, - \frac{\pi }{4}),( - 1,\frac{{3\pi }}{4})\)
The other two coordinates are\(( - 3,\frac{{13\pi }}{6}),(3,\frac{{7\pi }}{6})\)
The other two coordinates are\((1,2\pi - 1),( - 1,\pi - 1)\)

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Plotting the points

The polar plot for the point\((1,\frac{{7\pi }}{4})\) is shown below:

The coordinates \((r,\theta + 2n\pi ){\rm{ and }}(r,\theta )\)represent the same point.

Another coordinates for this point are\(\left( {1,\frac{{7\pi }}{4} - 2\pi } \right) = \left( {1, - \frac{\pi }{4}} \right)\)

The coordinates \(( - r,\theta + (2n + 1)\pi ){\rm{ and }}(r,\theta )\)represent the same point.

Another coordinates for this point are \(\left( { - 1,\frac{{7\pi }}{4} - \pi } \right) = \left( { - 1,\frac{{3\pi }}{4}} \right)\)

Step 2: Plotting the points

b. The polar plot for the point\(( - 3,\frac{\pi }{6})\)is shown below:

The coordinates \((r,\theta + 2n\pi ){\rm{ and }}(r,\theta )\)represent the same point.

Another coordinates for this point are\(\left( { - 3,\frac{\pi }{6} + 2\pi } \right) = \left( { - 3,\frac{{13\pi }}{6}} \right)\)

The coordinates \(( - r,\theta + (2n + 1)\pi ){\rm{ and }}(r,\theta )\)represent the same point.

Another coordinates for this point are \(\left( {3,\frac{\pi }{6} + \pi } \right) = \left( {3,\frac{{7\pi }}{6}} \right)\)

Step 2: Plotting the points

(c)The polar plot for the point\((1, - 1)\) is shown below:

The coordinates \((r,\theta + 2n\pi ){\rm{ and }}(r,\theta )\)represent the same point.

Another coordinates for this point are\((1,2\pi - 1)\)

The coordinates \(( - r,\theta + (2n + 1)\pi ){\rm{ and }}(r,\theta )\)represent the same point.

Another coordinates for this point are \(( - 1,\pi - 1)\)

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Essential Calculus: Early Transcendentals

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Short Answer

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with \(r > 0\)and one with \(r < 0\).
\(\begin{aligned}{l}(a)(1,7\pi /4)\\(b)( - 3,\pi /6)\\(c)(1, - 1)\end{aligned}\)

Step by Step Solution

Step 1: Plotting the points

Step 2: Plotting the points

Step 2: Plotting the points

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Essential Calculus: Early Transcendentals

Answers without the blur.

Short Answer

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with \(r > 0\)and one with \(r < 0\).\(\begin{aligned}{l}(a)(1,7\pi /4)\\(b)( - 3,\pi /6)\\(c)(1, - 1)\end{aligned}\)

Step by Step Solution

Step 1: Plotting the points

Step 2: Plotting the points

Step 2: Plotting the points

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Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with \(r > 0\)and one with \(r < 0\).
\(\begin{aligned}{l}(a)(1,7\pi /4)\\(b)( - 3,\pi /6)\\(c)(1, - 1)\end{aligned}\)