MHB Convert polar equation r= 1/1+sin(theta) to rectangular equation

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To convert the polar equation r = 1/(1 + sin(θ)) to rectangular form, start by manipulating the equation. Dividing both sides by r leads to the equation 1 = 1/(r + r sin(θ)), which simplifies to r + r sin(θ) = 1. This can be rewritten as r + y = 1, where y = r sin(θ). Finally, substituting r = √(x² + y²) into the equation results in x² + y² = (1 - y)². The final rectangular equation is x² + y² = (1 - y)².
Elissa89
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The equation is:

r= 1/1+sin(theta)

I know the answer is supposed to be:

x^2+y^2=(1-y)^2

I can't figure out the steps to get to the answer.
 
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Elissa89 said:
The equation is:

r= 1/1+sin(theta)

I know the answer is supposed to be:

x^2+y^2=(1-y)^2

I can't figure out the steps to get to the answer.

$r = \dfrac{1}{1+\sin{\theta}}$

divide both sides by $r$ ...

$1 = \dfrac{1}{r+r\sin{\theta}} \implies r+r\sin{\theta} = 1$

$r + y = 1$

$r = 1 - y$

can you finish?
 
skeeter said:
$r = \dfrac{1}{1+\sin{\theta}}$

divide both sides by $r$ ...

$1 = \dfrac{1}{r+r\sin{\theta}} \implies r+r\sin{\theta} = 1$

$r + y = 1$

$r = 1 - y$

can you finish?

Yes Thanks
 

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