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Q 46.

Found in: Page 731


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.

r=cos 4θ

The required equation is x2+y232=x2-3y2.

See the step by step solution

Step by Step Solution

Step 1. Given information.

The given equation in polar coordinates is:

r=cos 4θ

Step 2. Find the equation in rectangular coordinates.

r=cos 4θr=2 cos2 2θ-1 cos 4θ=2 cos2 2θ-1r=22cos2 2θ-1 -1 cos 2θ=2 cos2θ-1r=4 cos2θ-2-1r=4 cos2θ-3

Substitute xr=cosθ,

role="math" localid="1649323840721" r=4·x2r2-3r=4x2r2-3r=4x2-3r2r2

Cross multiply,

r3=4x2-3r2x2+y23=4x2-3x2+y2 r2=x2+y2 and r=x2+y2x2+y232=4x2-3x2-3y2x2+y232=x2-3y2

Therefore, the equation in rectangular coordinates is x2+y232=x2-3y2.

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