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Q15.

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Precalculus Mathematics for Calculus
Found in: Page 600
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

Testing for Symmetry Test the polar equation for symmetry to the polar axis, the pole, and the line θ=π/2

r2=4cos2θ .

The polar equation r2=4cos2θ is symmetric to the polar axis, the pole, and the lineθ=π2 .

See the step by step solution

Step by Step Solution

Step 1. Given information.

The given polar equation r2=4cos2θ.

Step 2. Finding given equation Symmetric or not.

If the polar equation r2=4cos2θ,(r,θ) can be replaced

by (r,θ) or (r,πθ) , then the graph is symmetric to the pole.

If the polar equation r2=4cos2θ,(r,θ) can be replaced by (r,θ) or (r,π+θ) , then the graph is symmetric to the pole.

If the polar equation r2=4cos2θ,(r,θ) can be replaced by (r,πθ) or (r,θ) , then the graph is symmetric to the line θ=π2.

The given polar equation is r2=4cos2θ

Testing for the symmetry of the line θ=π2 .

Replacing (r,θ)=(r,θ) and simplifying the equation

If the resulting equation r2=4cos2θ is equal to the original equation then it is symmetry about the lineθ=π2 .

Invalid <m:msup> element=4cos(2θ)r2=4cos2θ

The polar equation r2=4cos2θ is not symmetric to the line θ=π2 .

Step 3. Testing for symmetry about page polar axis.

Replacing (r,θ)=(r,θ) and simplifying the equation r2=4cos2θ then it is symmetry about the polar axis.

r2=4cos(2θ)r2=4cos2θ

The polar equation r2=4cos2θ is symmetric to the polar axis.

Step 4. Testing for symmetry about the pole.

Replacing (r,θ)=(r,θ) and simplifying the equation

If the resulting equation is equal to the original equation r2=4cos2θ is symmetric to the pole.

(r)2=4cos2θr2=4cos2θ

The polar equation r2=4cos2θ is symmetric to the pole.

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