How do you convert #r^2 = cost# to rectangular form?

We have:

and from this we can derive:

or:

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To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cosTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

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1.To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. (To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

2. ( rTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta )To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

3. ( r^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) forTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

4. ( r^2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for theTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

5. ( r^2 =To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the xTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

6. ( r^2 = xTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinateTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

7. ( r^2 = x^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate andTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

8. ( r^2 = x^2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and (To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

9. ( r^2 = x^2 +To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( yTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

10. ( r^2 = x^2 + yTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y =To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

11. ( r^2 = x^2 + y^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = rTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

12. ( r^2 = x^2 + y^2 \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sinTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

13. ( r^2 = x^2 + y^2 )To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

14. ( r^2 = x^2 + y^2 ) (To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

15. ( r^2 = x^2 + y^2 ) (fromTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

16. ( r^2 = x^2 + y^2 ) (from theTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta )To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

17. ( r^2 = x^2 + y^2 ) (from the conversionTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) forTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

18. ( r^2 = x^2 + y^2 ) (from the conversion ofTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for theTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

19. ( r^2 = x^2 + y^2 ) (from the conversion of polarTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the yTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

20. ( r^2 = x^2 + y^2 ) (from the conversion of polar toTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinateTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

21. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangularTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate inTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

22. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinatesTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polarTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

23. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates) To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinatesTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

24. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates) 2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

25. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates) 2.To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. (To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

SoTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So,To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cosTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, forTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\thetaTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( rTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta)To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) =To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 =To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \fracTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{xTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cosTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{rTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r}To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} )To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

SquareTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (fromTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sidesTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from theTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides toTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definitionTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to getTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition ofTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get (To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosineTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( rTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine inTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms ofTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 =To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polarTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinatesTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cosTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

SubTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equationTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 intoTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). UsingTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equationTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using theTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the PyTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the PythagTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the PythagoreanTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

(To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identityTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( xTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity (To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cosTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 +To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + yTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 =To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta +To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = rTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sinTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 =To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cosTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta =To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\thetaTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

ThereforeTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substituteTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore,To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute (To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, theTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangularTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular formTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 -To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form ofTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of theTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sinTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation isTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is (To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta )To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 +To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) forTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + yTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for (To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 =To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cosTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cosTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cos(\To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \thetaTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cos(\thetaTo convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \theta \To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cos(\theta)To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \theta ). To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cos(\theta) \To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \theta ). NowTo convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cos(\theta) ).To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \theta ). Now,To convert the equation ( r^2 = \cos(\theta) ) to rectangular form, use the relationships between polar and rectangular coordinates:

1. ( r^2 = x^2 + y^2 ) (from the conversion of polar to rectangular coordinates)
2. ( \cos(\theta) = \frac{x}{r} ) (from the definition of cosine in terms of polar coordinates)

Substitute equation 2 into equation 1:

( x^2 + y^2 = r^2 = \cos(\theta) )

Therefore, the rectangular form of the equation is ( x^2 + y^2 = \cos(\theta) ).To convert ( r^2 = \cos \theta ) to rectangular form, use the trigonometric identity ( x = r \cos \theta ) for the x-coordinate and ( y = r \sin \theta ) for the y-coordinate in polar coordinates.

So, for ( r^2 = \cos \theta ):

Square both sides to get ( r^2 = \cos^2 \theta ). Using the Pythagorean identity ( \cos^2 \theta + \sin^2 \theta = 1 ), substitute ( 1 - \sin^2 \theta ) for ( \cos^2 \theta ). Now, you have ( r^2 = 1 - \sin^2 \theta ). Rearrange the equation to isolate ( \sin^2 \theta ): ( \sin^2 \theta = 1 - r^2 ). Take the square root of both sides to solve for ( \sin \theta ): ( \sin \theta = \sqrt{1 - r^2} ).

Now, you have the values for ( \cos \theta ) and ( \sin \theta ). You can use these values to convert to rectangular form:

[ x = r \cos \theta ] [ x = r \sqrt{\cos^2 \theta} ] [ x = r \sqrt{1 - \sin^2 \theta} ] [ x = r \sqrt{1 - (1 - r^2)} ] [ x = r \sqrt{r^2} ] [ x = r^2 ]

So, ( r^2 = \cos \theta ) in polar form can be converted to ( x = r^2 ) in rectangular form.