Hi, my name is Tran Trung
This question is secondary school
The question's for me.

How do I convert r = 2/(2sin(theta) - 3cos(theta)) to rectangular and x2 + y2 -2y = 0 to polar form?

thank you

Hi Tran,

The key to converting to and from polar coordinates are the exprressions

x = r cos(theta)
y = r sin(theta)

Your second problem (Cartesian to polar) is direct since you can substitute the expressions above into the equation that you have and then simplify. That is

x2 + y2 -2y = 0
r2cos2(theta) + r2sin2(theta)-2 r sin(theta) = 0

Now simplif using the fact that sin2(theta) + cos2(theta) = 1.

For your first problem write sin(theta) = y/r and cos(theta) = x/r and then simplify. You will find that the symbol r can be eliminated and you are left with an expression involving only the variables x and y.

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