Rewriting polar coordinates as rectangular coordinates?

[ChristaJoy]

I have r=sin(theta)+1, and I need to convert it into rectangular coordinates with (x,y). I know that rsin(theta)=y and rcos(theta)=x, and that x^2+y^2=r^2, but I don't know how to use this information to find x and y.

Could anyone tell me the first couple steps please? Thank you muchly!

 

[soroban]

Hello, ChristaJoy!

\(\displaystyle \text{Convert to rectangular cooredinates: }\:r \:=\:\sin\theta +1\)

Multiply by \(\displaystyle r\!:\;\;r^2 \:=\:r\sin\theta + r\)

Substitute: ..\(\displaystyle x^2 + y^2 \:=\:y + \sqrt{x^2+y^2}\)

 

[Deleted member 4993]

Another way:

y = r * sinΘ and r = √(x² + y²) → sinΘ = y/√(x² + y²)

then

r = sinΘ + 1 → √(x² + y²) = y/√(x² + y²) + 1 ... and simplify...

 

[ChristaJoy]

Hello, ChristaJoy!


Multiply by \(\displaystyle r\!:\;\;r^2 \:=\:r\sin\theta + r\)

Substitute: ..\(\displaystyle x^2 + y^2 \:=\:y + \sqrt{x^2+y^2}\)

After simplifying a little bit, I got to this:

x^2(x^2-1)+y^2(y^2-2)=0

Am I on the right track?

 

[Deleted member 4993]

After simplifying a little bit, I got to this:

x^2(x^2-1)+y^2(y^2-2)=0

Am I on the right track? .... No

How did you get there? Please show work.