The polar equation r = 1/(1 + sin(θ)) can be converted to the rectangular equation x² + y² = (1 - y)². The conversion process involves dividing both sides by r, leading to the equation 1 = 1/(r + r sin(θ)), which simplifies to r + y = 1. This indicates that r can be expressed as r = 1 - y, facilitating the transition from polar to rectangular coordinates.
PREREQUISITESStudents in mathematics, particularly those studying calculus or analytical geometry, as well as educators looking for clear examples of polar to rectangular conversions.
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.
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?