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Q16.

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Precalculus Mathematics for Calculus

Found in: Page 592

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Different Polar Coordinates for the Same Point Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with $r < 0$ and the other with $r > 0$ $(3, 1)$

The graph of a given point,

The other two points are, $(- 3, 1 + π)$ $(3, 1 + 2 π)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

A point in polar coordinates as $(3, 1)$

Step 2. Concept used

The point is plotted or presented on a graph using the polar coordinate system. The radius is represented by the first coordinate, while the angle is represented by the second.

Step 3. Calculation

Now plot the point on the graph,

Now for $r > o$ , add $2 π$ into the coordinate-

$\Rightarrow (3, 1 + 2 π)$

For $r < o$ , change the sign of radius and add $π$ to angle given-

$\Rightarrow (- 3, 1 + π)$

Most popular questions for Math Textbooks

Different Polar Coordinates for the Same Point Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with $r < 0$ and the other with $r > 0$ $(2, \frac{3 π}{4})$

Points in Polar Coordinates Determine which point in the figure, $P, Q, R & S$ , has the given polar coordinates $(4, \frac{3 π}{4})$

Yes or No? If No, give a reason.

Do the polar coordinates $(2, \frac{π}{6})$ and $(- 2, \frac{7 π}{6})$ represent the same point?

Graphs of Polar Equations Match the polar equation with the graphs labeled I-VI. Use the table on page 519 to help you.

. $r = \sin 3 θ$

Polar Equations to Rectangular Equations

Convert the polar equation to rectangular coordinates

$r = 4 \sin θ$

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