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Chapter 9: Q. 75 (page 568)

The letters r and 胃represent polar coordinates. Write each equation using rectangular coordinates x,y.

r=cos胃

Short Answer

Expert verified

The equation is written using rectangular coordinates asx2+y2-x=0.

Step by step solution

01

Step 1. Given Information

We are given an equation r=cos胃.

We need to write the equation using rectangular coordinates.

02

Step 2. Concept Used

If P is a point with polar coordinates r,胃, the rectangular coordinates x,y of P are given by

x=rcos胃y=rsin胃

And it implies that

x2+y2=r2

03

Step 3. Convert into rectangular coordinates   

In the given equation r=cos胃multiply both sides by r.

r路r=r路cos胃r2=rcos胃

Now using the relations substitute x2+y2for r2and xfor rcos胃we get

r2=rcos胃x2+y2=xx2+y2-x=0

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