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

Elissa89

Member
Oct 19, 2017
52
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.
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
644
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?
 

Elissa89

Member
Oct 19, 2017
52
$r = \dfrac{1}{1+\sin{\theta}}$

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