Question

Convert R=(12)/4+8sin the theta to rectangular form

Answer 1

`r=(12)/(4+8\sin\theta)=\frac3{1+2\sin\theta}`

Let
`y=2\sin\theta`, and recall that in polar coordinates,
`r=√(x^2+y^2)`. This means you have


`√(x^2+y^2)=\frac3{1+y}`

You can stop there, or try to find something that looks somewhat nicer.


`x^2+y^2=\frac9{(1+y)^2}`