Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Identify and graph each polar equation. Verify your graph using a graphing utility.
$r = 3 \cos (4 θ)$

The equation $r = 3 \cos (4 θ)$ is a rose with eight petals and the graph is

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given equation is

$r = 3 \cos (4 θ)$

Step 2. Symmetry with the polar axis

Substitute $- θ$ for $θ$ in the equation

$r = 3 \cos (4 (- θ)) r = 3 \cos (4 θ)$

The equation matches with the original equation so the test is satisfied.

the graph is symmetric with respect to the polar axis

Step 3. Symmetry with line θ=π2

Substitute $π - θ$ for $θ$ in the equation

role="math" localid="1646686393219" $r = 3 \cos (4 (π - θ)) r = 3 \cos (4 π - 4 θ) r = 3 \cos (4 θ)$

The equation matches the original equation so the test is satisfied.

the graph is symmetric with respect to the line $θ = \frac{π}{2}$

Step 4. Symmetry with the pole

The equation is symmetric with respect to the polar axis and line $θ = \frac{π}{2}$

so the equation is symmetric with respect to the pole

Step 5. Points for the graph

Consider different values for $θ$ in interval $(0, \frac{π}{2})$ and determine coordinates of several points for graph

Step 6. Graph of the equation

Locates points and use them to plot the graph of the equation

The graph state that the equation is a rose with eight petals

Step 7. Verification

Plot the graph of the equation $r = 3 \cos (4 θ)$ using a graphing utility

Graph matches so our graph is correct.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Identify and graph each polar equation. Verify your graph using a graphing utility.
$r = 3 \cos (4 θ)$

Step by Step Solution

Step 1. Given Information

Step 2. Symmetry with the polar axis

Step 3. Symmetry with line θ=π2

Step 4. Symmetry with the pole

Step 5. Points for the graph

Step 6. Graph of the equation

Step 7. Verification

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Identify and graph each polar equation. Verify your graph using a graphing utility.r=3 cos4θ

Step by Step Solution

Step 1. Given Information

Step 2. Symmetry with the polar axis

Step 3. Symmetry with line θ=π2

Step 4. Symmetry with the pole

Step 5. Points for the graph

Step 6. Graph of the equation

Step 7. Verification

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Identify and graph each polar equation. Verify your graph using a graphing utility.
$r = 3 \cos (4 θ)$