# How do you change the polar equation #r(2+costheta)=1# into rectangular form?

supplying the pass formulas

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To convert the polar equation ( r(2+\cos(\theta))=1 ) into rectangular form, you can use the following steps:

- Substitute ( r = \sqrt{x^2 + y^2} ) and ( \cos(\theta) = \frac{x}{\sqrt{x^2 + y^2}} ) into the polar equation.
- Simplify the equation.
- Rearrange the equation to isolate ( y ), if necessary.

So, substituting into the equation:

[ \sqrt{x^2 + y^2} (2 + \frac{x}{\sqrt{x^2 + y^2}}) = 1 ]

Simplify the equation:

[ 2\sqrt{x^2 + y^2} + x = 1 ]

Rearrange to isolate ( y ):

[ 2\sqrt{x^2 + y^2} = 1 - x ]

[ \sqrt{x^2 + y^2} = \frac{1 - x}{2} ]

[ x^2 + y^2 = \left(\frac{1 - x}{2}\right)^2 ]

[ x^2 + y^2 = \frac{1 - 2x + x^2}{4} ]

[ 4x^2 + 4y^2 = 1 - 2x + x^2 ]

[ 3x^2 + 4y^2 + 2x - 1 = 0 ]

Therefore, the rectangular form of the polar equation ( r(2+\cos(\theta))=1 ) is ( 3x^2 + 4y^2 + 2x - 1 = 0 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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